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AUTHORS Normal file
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Copyright © 2021 European University at St. Petersburg and Skolkovo Institute of Science and Technology
Moral rights:
Kirill Polovnikov
Nikita Pospelov
Dmitriy Skougarevskiy
The version control system provides attribution for specific lines of code.

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cff-version: 1.2.0
message: "If you use this algorithm, please cite it as below."
authors:
- family-names: "Polovnikov"
given-names: "Kirill"
orcid: "https://orcid.org/0000-0001-9903-9623"
- family-names: "Pospelov"
given-names: "Nikita"
- family-names: "Skougarevskiy"
given-names: "Dmitriy"
orcid: "0000-0002-4022-6210"
title: "α-Indirect Control in Onion-like Networks"
date-released: 2021-09-16
year: 2021
url: "https://github.com/eusporg/alphaicon"
preferred-citation:
type: unpublished
authors:
- family-names: "Polovnikov"
given-names: "Kirill"
orcid: "https://orcid.org/0000-0001-9903-9623"
- family-names: "Pospelov"
given-names: "Nikita"
- family-names: "Skougarevskiy"
given-names: "Dmitriy"
orcid: "0000-0002-4022-6210"
url: "https://arxiv.org/abs/2109.07181"
title: "α-Indirect Control in Onion-like Networks"
year: 2021

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DEPENDENCIES Normal file
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Imports:
data.table (>= 1.13.2),
stringi (>= 1.4.4),
stringr (>= 1.3.1),
lubridate (>= 1.7.10),
remotes (>= 2.3.0),
usethis (>= 2.0.1),
ndjson (>= 0.8.0),
igraph (>= 1.2.6),
Matrix (>= 1.3-3),
matrixStats (>= 0.59.0),
stargazer (>= 5.2.1),
fastDummies (>= 1.6.3),
ggplot2 (>= 3.3.3),
ggthemes (>= 4.2.4),
ggrepel (>= 0.9.1),
ggnetwork (>= 0.5.9),
showtext (>= 0.9-2)

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# List of R dependencies for the project
DEPENDENCIES:
# Do nothing, the file is created outside the repo
noop
# Helper function to install the dependencies
code/helper_functions/install_dependencies.r:
# Do nothing, the file is created outside the repo
noop
# People with Significant Control snapshot from Companies House
data/uk/persons-with-significant-control-snapshot-2021-08-02.txt:
# Do nothing, the file is created outside the repo
noop
# Company Data Product snapshot from Companies House
data/uk/BasicCompanyDataAsOneFile-2021-08-01.csv:
# Do nothing, the file is created outside the repo
noop
# Industry sector names
data/uk/sic_2007_code_list.csv:
# Do nothing, the file is created outside the repo
noop
# CorpWatch SEC 10-K filings data: company name-id mapping
data/corpwatch_api_tables_csv_14aug21/cik_name_lookup.csv:
# Do nothing, the file is created outside the repo
noop
# CorpWatch SEC 10-K filings data: basic company information
data/corpwatch_api_tables_csv_14aug21/company_info.csv:
# Do nothing, the file is created outside the repo
noop
# CorpWatch SEC 10-K filings data: company locations
data/corpwatch_api_tables_csv_14aug21/company_locations.csv:
# Do nothing, the file is created outside the repo
noop
# Process the PSC snapshot
data/uk/psc_snapshot_2021-08-02.rdata: data/uk/persons-with-significant-control-snapshot-2021-08-02.txt
Rscript code/data_preparation/uk/1a_process_psc_snapshot.r
# Process the live snapshot of companies data
data/uk/uk_basic_companies_data_2021-08-01.rdata: data/uk/BasicCompanyDataAsOneFile-2021-08-01.csv data/uk/sic_2007_code_list.csv
Rscript code/data_preparation/uk/1b_process_companies_data.r
# Convert the PSC snapshot to a company-participant clean data
output/uk/uk_organisations_participants_2021_long_2aug21.csv: data/uk/psc_snapshot_2021-08-02.rdata data/uk/uk_basic_companies_data_2021-08-01.rdata
Rscript code/data_preparation/uk/2_psc_snapshot_to_participants_panel
# Create SEC 10-K Exhibit 21 company-participant evaluation set matched to PSC and live companies
data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv: data/corpwatch_api_tables_csv_14aug21/company_info.csv data/corpwatch_api_tables_csv_14aug21/cik_name_lookup.csv data/corpwatch_api_tables_csv_14aug21/company_locations.csv data/uk/psc_snapshot_2021-08-02.rdata data/uk/uk_basic_companies_data_2021-08-01.rdata
Rscript code/data_preparation/uk/3_prepare_affiliated_entities_evaluation_data.r
# Classify the network into SH, ST, C, and I entities
output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv: output/uk/uk_organisations_participants_2021_long_2aug21.csv
jupyter nbconvert --ExecutePreprocessor.timeout=-1 --execute code/alphaicon_paper/1_compute_alphaicon.ipynb
# Compute the shares by transitivity
transitiveshares := $(wildcard output/uk/transitive/uk_organisations_transitive_ownership_alpha*.csv)
$(transitiveshares): output/uk/uk_organisations_participants_2021_long_2aug21.csv output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv
jupyter nbconvert --ExecutePreprocessor.timeout=-1 --execute code/alphaicon_paper/1_compute_alphaicon.ipynb
# Helper function implementing NPI/DPI computation
code/helper_functions/compute_power_index.r:
# Do nothing, the file is created outside the repo
noop
# Compute the DPI shares
output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv: code/helper_functions/compute_power_index.r
Rscript code/alphaicon_paper/2_compute_npi_dpi.r
# Compute the NPI shares
output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv: code/helper_functions/compute_power_index.r
Rscript code/alphaicon_paper/2_compute_npi_dpi.r
# Perform the evaluation of algorithms at different k
output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall.csv: output/uk/uk_organisations_participants_2021_long_2aug21.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv $(transitiveshares) output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv
Rscript code/alphaicon_paper/5_algorithm_evaluation.r
# Perform the evaluation of algorithms at different path length
output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall_by_pathlength.csv: output/uk/uk_organisations_participants_2021_long_2aug21.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv $(transitiveshares) output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv
Rscript code/alphaicon_paper/5_algorithm_evaluation.r
# Create the ranking of top-100 holders by each method
output/alphaicon_paper/uk_organisations_top100_holders_2021_long_2aug21.csv: output/uk/uk_organisations_participants_2021_long_2aug21.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv $(transitiveshares) output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv
Rscript code/alphaicon_paper/6_rank_top_holders.r
# Compute Kendall's tau-b rank correlation of per-company participants for different methods
output/alphaicon_paper/kendall_taus_participant_ranks_dpi_npi_transitive_uk_organisations_participants_2021_7sep21.csv: output/uk/uk_organisations_participants_2021_long_2aug21.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv $(transitiveshares) output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv
Rscript code/alphaicon_paper/6_rank_top_holders.r
# α-ICON paper
alphaicon_paper: output/alphaicon_paper/uk_organisations_top100_holders_2021_long_2aug21.csv output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall.csv output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall_by_pathlength.csv DEPENDENCIES
Rscript code/helper_functions/install_dependencies.r
Rscript code/helper_functions/compute_power_index.r
Rscript code/alphaicon_paper/3_summary_stat_by_node_type.r
Rscript code/alphaicon_paper/4_illustrate_algorithm.r
Rscript code/alphaicon_paper/5_algorithm_evaluation.r
Rscript code/alphaicon_paper/6_rank_top_holders.r

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<table>
<tbody>
<tr>
<td valign="top" width=200><img src="https://user-images.githubusercontent.com/3776887/133301237-145e43f0-d4b3-4ae5-bf15-113efc2ad189.png"></td>
<td valign="top"><h1>α-Indirect Control in Onion-like Networks</h1>
We propose a fast, accurate, and scalable algorithm to detect ultimate controlling entities in global corporate networks. α-ICON uses company-participant links to identify super-holders who exert control in networks with millions of nodes.<br><br>
By exploiting onion-like properties of such networks we iteratively peel off the hanging vertices until a dense core remains. This procedure allows for a dramatic speed-up, uncovers meaningful structures, and handles circular ownership by design.<br><br>
Read our <a href="https://arxiv.org/abs/2109.07181" target="_blank">paper</a> with the applications. As a toy example, consider the below corporate network where α-ICON designates Mr Philip Mactaggart (in green) as the super-holder exerting control over all other entities, directly or indirectly held:
</td>
</tr>
</tbody>
</table>
<img src="https://user-images.githubusercontent.com/3776887/133299028-152f030a-e1c7-428b-83ef-e5f4e92414bc.png">
## Installation
To replicate the analysis you need to clone this repository to your local machine. Then you need to install the required versions of R dependencies listed in `DEPENDENCIES`. `code/helper_functions/install_dependencies.r` automates this step, but you may still need to install the underlying libraries manually with [Homebrew](https://brew.sh) or `apt-get`, depending on your platform. Finally, you need to declare the environment variable `ALPHAICON_PATH` in bash pointing to the repository. Or, better yet, you can add it in your `.Renviron` with
```console
user:~$ echo 'ALPHAICON_PATH="path_to_cloned_repository"' >> ~/.Renviron
```
The repository does not contain any data due to its size (10+ GB unpacked); most files in `data/` and `output/` folders are zero-byte placeholders. We provide a <a href="https://drive.google.com/drive/folders/10Tq-b4BVsG3gmq2JVa026Nilzj8eojNB" target="_blank">public Google Drive folder</a> with the populated `data/` and `output/` directories. You may still need to unzip them manually.
A self-contained example of α-ICON is also available in <a href="https://colab.research.google.com/drive/1AvO8hJzwj2LoKsyxk5LfSWK7LW1U02Mc" target="_blank">Google Colaboratory</a>.
## Repository structure
```
data/
├─uk/ # Data on UK companies and participants
| ├ persons-with-significant-control-snapshot-2021-08-02.txt # Source PSC data
| ├ BasicCompanyDataAsOneFile-2021-08-01.csv # Source data on live companies in UK
| ├ sic_2007_code_list.csv # Standard Industrial Classification codes
| ├ psc_snapshot_2021-08-02.rdata # Processed People with Significant Control data
| └ uk_basic_companies_data_2021-08-01.rdata # Processed Basic Company data
|
├─corpwatch_api_tables_csv_14aug21/ # Data from CorpWatch Dump
| ├ company_info.csv # Source companies data from SEC filings
| ├ cik_name_lookup.csv # Company name variants in SEC filings
| └ company_locations.csv # Company locations in SEC filings
|
code/
├─helper_functions/
| ├ install_dependencies.r # Installs R dependencies used in the project
| └ compute_power_index.r # Computes Mizuno et al. (2020) DPI and NPI
|
├─data_preparation/
| └─uk/
| ├ 1a_process_psc_snapshot.r # Prepare source PSC data
| ├ 1b_process_companies_data.r # Prepare source data on live companies
| ├ 2_psc_snapshot_to_participants_panel.r # PSC data to entity-participant info
| └ 3_prepare_affiliated_entities_evaluation_data.r # Process CorpWatch data
|
├─alphaicon_paper/
| ├ 1_compute_alphaicon.ipynb # Jupyter Notebook w. α-ICON (also on Google Colab)
| ├ 2_compute_npi_dpi.r # Computation of Direct and Network Power Indices
| ├ 3_summary_stat_by_node_type.r # UK PSC network statistics by core/SH/ST/I
| ├ 4_illustrate_algorithm.r # Visualise selected networks
| ├ 5_algorithm_evaluation.r # Compute recall @ k and l for various algorithms
| └ 6_rank_top_holders.r # Examine the rankings of super-holders & Kendall's tau
|
output/
├─uk/
| ├ uk_organisations_participants_2021_long_2aug21.csv # Primary ownership data
| ├ uk_organisations_participation_graph_core_periphery_membership_6aug21.csv
| ├─npi_dpi/ # Mizuno et al. (2020) computation results on UK PSC data
| | └─10000iter/
| | ├ uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv # DPI
| | └ uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv # NPI
| |
| ├─transitive/ # Computed α-ICON shares on equity shares or DPI weights
| | ├ uk_organisations_transitive_ownership_alpha*_2021_long_2aug21.csv # α = *
| | └ uk_organisations_transitive_ownership_alpha*_2021_long_7sep21_dpi_....csv
| |
└─alphaicon_paper/
├ uk_orgs_algorithm_evaluation_recall.csv # Algorithm recall by k
├ uk_orgs_algorithm_evaluation_recall_by_pathlength.csv # Algorithm recall by l
├ uk_organisations_top100_holders_2021_long_2aug21.csv # Top SH in PSC network
├ uk_organisations_top100_holders_diff_npi_dpi_2021_long_2aug21.csv # Top-100 SH
| # with the largest difference betw. total DPI and NPI
├ uk_organisations_top100_holders_diff_transitive_dpi_2021_long_2aug21.csv
| # Top-100 SH with the largest difference betw. total DPI and α-ICON (α=0.999)
├ uk_organisations_top100_holders_diff_transitive_npi_2021_long_2aug21.csv
| # Top-100 SH with the largest difference betw. total NPI and α-ICON (α=0.999)
└ network_examples/ # Visualisations of selected networks
```
We provide an annotated `Makefile` that documents the data analysis in our papers.
To build the ‘<a href="https://arxiv.org/abs/2109.07181" target="_blank">α-Indirect Control in Onion-like Networks</a>’ paper run `make alphaicon_paper` when in the repository folder.
Please note that those commands will not produce any publication-ready output files (e.g. tables or figures): the export statements are commented out in the code. Our intention is to make the analysis pipeline transparent to the readers with the aid of `make`:
![alphaicon_dependencies](https://user-images.githubusercontent.com/3776887/133301812-87f25078-de5a-4bea-b9b0-0e6addb51b2b.png)
## Licence
<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br />
Creative Commons License Attribution 4.0 International (CC BY 4.0).
Copyright © the respective contributors, as shown by the `AUTHORS` file.
People with Significant Control data is <a href="http://download.companieshouse.gov.uk/en_pscdata.html">distributed</a> by Companies House under <a href="https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/">Open Government Licence v3.0</a>.
Free Company Data Product is <a href="http://download.companieshouse.gov.uk/en_output.html">distributed</a> by Companies House under <a href="https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/">Open Government Licence v3.0</a>.
## Contacts
Dmitriy Skougarevskiy, Ph.D.
dskougarevskiy@eu.spb.ru

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# This code computes Direct Power Index and
# Network Power Index Mizuno, Doi, and Kurizaki (2020, p. 7)
# (https://doi.org/10.1371/journal.pone.0237862)
# for the UK entities in PSC data
library(data.table)
# NB: there seems to be a bug in multi-threaded data.table group
# processing in Windows: https://github.com/Rdatatable/data.table/issues/4294
setDTthreads(1)
set.seed(42)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Load the function to compute power index
source("code/helper_functions/compute_power_index.r")
# Load British entities data
uk_entities <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", colClasses = c("character", "character", "factor", "numeric"), encoding = "UTF-8", na.strings = "")
uk_entities[, kind := NULL ]
gc()
# Remove self-loops and missing equity shares
uk_entities <- uk_entities[ participant_id != company_number & !is.na(equity_share) ]
# Normalize equity to one
uk_entities[, equity_share := 100*equity_share/sum(equity_share), by = "company_number" ]
# Run DPI computation on 10000 iterations
tic <- Sys.time()
uk_entities_dpi_10000iter <- compute_power_index(uk_entities,
participant_var = "participant_id",
entity_var = "company_number",
weight_var = "equity_share",
iterations = 10000,
powerindex = "dpi",
quota = 50,
save_labels = FALSE
)
toc <- Sys.time()
toc - tic # Takes 2.353837 days on Intel Xeon E5-2620
fwrite(uk_entities_dpi_10000iter, file = paste0("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv"), eol = "\n")
# Run NPI computation on 10000 iterations
tic <- Sys.time()
uk_entities_npi_10000iter <- compute_power_index(uk_entities,
participant_var = "participant_id",
entity_var = "company_number",
weight_var = "equity_share",
iterations = 10000,
powerindex = "npi",
quota = 50,
epsilon = 0.01,
iterations_to_discard = 1000,
save_labels = FALSE
)
toc <- Sys.time()
toc - tic # Takes 3.755192 days on Intel Xeon E5-2620
fwrite(uk_entities_npi_10000iter, file = paste0("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv"), eol = "\n")

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# This code creates summary statistics
# table by node type for the α-ICON paper
library(data.table)
library(stringi)
library(stringr)
library(lubridate)
library(igraph)
library(stargazer)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
############
# Data loading
# Load the active participants snapshot of PSC (prepared by data_preparation/uk/2_psc_snapshot_to_participants_panel.r)
psc <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
setnames(psc, "equity_share", "share")
psc[, share := share/100]
psc <- psc[ company_number != participant_id & !is.na(share) ]
# Load the companies data (prepared by data_preparation/uk/1b_process_companies_data.r)
load("data/uk/uk_basic_companies_data_2021-08-01.rdata")
# Shorter industry names
uk_basic_companies_data[ industrysection_1 == "Financial and insurance activities", industrysection_1 := "Finance/Insurance"]
uk_basic_companies_data[ industrysection_1 == "Information and communication", industrysection_1 := "IT"]
uk_basic_companies_data[ industrysection_1 == "Other service activities", industrysection_1 := "Other service"]
uk_basic_companies_data[ industrysection_1 == "Professional, scientific and technical activities", industrysection_1 := "Profess./Science activ"]
uk_basic_companies_data[ industrysection_1 == "Mining and Quarrying", industrysection_1 := "Mining/Quarrying"]
uk_basic_companies_data[ industrysection_1 == "Mining and Quarrying", industrysection_1 := "Mining/Quarrying"]
uk_basic_companies_data[ industrysection_1 == "Real estate activities", industrysection_1 := "Real estate"]
uk_basic_companies_data[ industrysection_1 == "Arts, entertainment and recreation", industrysection_1 := "Arts/Entertainment"]
uk_basic_companies_data[ industrysection_1 == "Administrative and support service activities", industrysection_1 := "Admin./Support activ"]
uk_basic_companies_data[ industrysection_1 == "Accommodation and food service activities", industrysection_1 := "Hospitality/Food"]
uk_basic_companies_data[ industrysection_1 == "Human health and social work activities", industrysection_1 := "Health/Social work"]
uk_basic_companies_data[ industrysection_1 == "Wholesale and retail trade; repair of motor vehicles and", industrysection_1 := "Trade"]
uk_basic_companies_data[ industrysection_1 == "Transportation and storage", industrysection_1 := "Transportation/Storage"]
uk_basic_companies_data[ industrysection_1 == "Agriculture, Forestry and Fishing", industrysection_1 := "Agriculture"]
uk_basic_companies_data[ industrysection_1 == "Activities of households as employers; undifferentiated", industrysection_1 := "Households as employers"]
uk_basic_companies_data[ industrysection_1 == "Water supply, sewerage, waste management and", industrysection_1 := "Water/Sewerage/Waste"]
uk_basic_companies_data[ industrysection_1 == "Public administration and defence; compulsory social", industrysection_1 := "Public admin/Defence"]
uk_basic_companies_data[ industrysection_1 == "Electricity, gas, steam and air conditioning supply", industrysection_1 := "Electricity/Gas/Steam"]
uk_basic_companies_data[ industrysection_1 == "Activities of extraterritorial organisations and", industrysection_1 := "Extraterritorial orgs"]
# Company age
uk_basic_companies_data[, age := as.numeric(ymd("2021-08-01") - IncorporationDate)/31/12 ]
# Load the transitive ownership of each participant at alpha = 0.999
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
holders <- fread("output/uk/transitive/uk_organisations_transitive_ownership_alpha0.999_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", colClasses = c("character", "character", "numeric"))
# Load the data on graph membership
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
graph_membership <- fread("output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", header = T, colClasses = c("numeric", "character", "factor"))
graph_membership[, V1 := NULL ]
setnames(graph_membership, "company_number/id", "participant_id")
gc()
# Load the data for evaluation of the algorithms (prepared by data_preparation/uk/3_prepare_affiliated_entities_evaluation_data.r)
affiliated_entities <- fread("data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
# Remove the CorpWatch entity identifiers
affiliated_entities[, c("subsidiary_cw_id", "parent_cw_id") := NULL ]
# Add the data on the shortest paths from parent to subsidiary
psc_graph <- graph_from_data_frame(psc[participant_id != company_number & !is.na(share), c("participant_id", "company_number", "share"), with = F], directed = T)
# Compute all the distances on the graph
# from parent companies in the gold standard
# data to the subsidiates
affiliated_distance_mat <- distances(psc_graph, v = which(V(psc_graph)$name %in% unique(affiliated_entities$participant_id)), to = which(V(psc_graph)$name %in% affiliated_entities$company_number), mode = "out")
# Arrange them so that the distance is on the main diagonal
affiliated_distance <- as.data.table(as.table(affiliated_distance_mat))
names(affiliated_distance) <- c("participant_id", "company_number", "path_length")
# Remove non-reachable entries
affiliated_distance <- affiliated_distance[ is.finite(path_length) ]
# Add the path lengths to the affiliated entities data
affiliated_entities <- merge(affiliated_entities, affiliated_distance, by = c("company_number", "participant_id"), all.x = T, all.y = F, sort = F)
#nrow(affiliated_entities[!is.na(path_length)] # 1007
# Keep only matched orgs
affiliated_entities <- affiliated_entities[!is.na(path_length)]
############
# Graph membership data preparation
# Add the selected characteristics to the graph membership data
## Is entity or individual dummy
graph_membership[, kind := psc[ match(graph_membership$participant_id, psc$participant_id)]$kind ]
graph_membership[is.na(kind) & participant_id %in% psc$company_number, kind := "entity" ]
graph_membership <- graph_membership[ !is.na(kind) ]
graph_membership[, is_person := NA_real_ ]
graph_membership[ !is.na(kind), is_person := 0]
graph_membership[ kind == "individual", is_person := 1]
## Industry
graph_membership[, industrysection := uk_basic_companies_data[ match(graph_membership$participant_id, uk_basic_companies_data$CompanyNumber)]$industrysection_1 ]
## Add individuals to the said list
graph_membership[ is_person == 1, industrysection := "Individual"]
## Company age
graph_membership[, age := uk_basic_companies_data[ match(graph_membership$participant_id, uk_basic_companies_data$CompanyNumber)]$age ]
## Is public company
graph_membership[, companytype := uk_basic_companies_data[ match(graph_membership$participant_id, uk_basic_companies_data$CompanyNumber)]$CompanyCategory ]
graph_membership[, is_public := NA_real_ ]
graph_membership[!is.na(companytype) | is_person == 1, is_public := 0 ]
graph_membership[ companytype %in% c("Public Limited Company"), is_public := 1]
uk_basic_companies_data[, is_public := NA_real_ ]
uk_basic_companies_data[!is.na(CompanyCategory), is_public := 0 ]
uk_basic_companies_data[ CompanyCategory %in% c("Public Limited Company"), is_public := 1]
## Is in validation data
graph_membership[, in_validation := 0 ]
graph_membership[ participant_id %in% affiliated_entities$company_number | participant_id %in% affiliated_entities$participant_id, in_validation := 1 ]
uk_basic_companies_data[, in_validation := 0 ]
uk_basic_companies_data[ CompanyNumber %in% c(affiliated_entities$company_number, affiliated_entities$participant_id), in_validation := 1 ]
## In- and outdegree
psc_graph_degree <- data.table(participant_id = V(psc_graph)$name, indegree = degree(psc_graph, mode = "in"), outdegree = degree(psc_graph, mode = "out"))
graph_membership <- merge(graph_membership, psc_graph_degree, by = "participant_id", all.x = T, all.y = F, sort = T)
uk_basic_companies_data <- merge(uk_basic_companies_data, psc_graph_degree, by.x = "CompanyNumber", by.y = "participant_id", all.x = T, all.y = F, sort = F)
############
# Compute summary stat by graph membership
## Industry shares by type in PSC graph
industry_by_graphtype <- graph_membership[, list(N = .N), by = c("type", "industrysection") ]
industry_by_graphtype[ is.na(N), N := 0 ]
industry_by_graphtype[, percent := round(100*N/sum(N), 2), by = "type"]
# Add the total
industry_by_graphtype <- rbind(industry_by_graphtype, data.table(industrysection = "Total", industry_by_graphtype[, list( N = sum(N)), by = "type"], percent = 100))
## Industry shares in the company universe
industry_universe <- uk_basic_companies_data[, list(N_universe = .N), by = c("industrysection_1") ]
setnames(industry_universe, "industrysection_1", "industrysection")
industry_universe[ is.na(N_universe), N_universe := 0 ]
industry_universe[, percent_universe := round(100*N_universe/sum(N_universe), 2)]
# Add the total
industry_universe <- rbind(industry_universe, data.table( industrysection = "Total", N_universe = sum(industry_universe$N), percent_universe = 100), fill = T)
## Industry shares in the validation data
industry_validation <- graph_membership[ in_validation == 1, list(N_validation = .N), by = c("industrysection") ]
industry_validation[ is.na(N_validation), N_validation := 0 ]
industry_validation[, percent_validation := round(100*N_validation/sum(N_validation), 2)]
# Add the total
industry_validation <- rbind(industry_validation, data.table( industrysection = "Total", N_validation = sum(industry_validation$N), percent_validation = 100), fill = T)
# Compute means of in/outdegree by type, for the entire universe, and for validation data
means_by_graphtype <- graph_membership[, lapply(.SD, mean, na.rm = T), .SDcols = c("indegree", "outdegree", "age", "is_public"), by = "type" ]
means_by_graphtype[, industrysection := "tempname" ]
means_by_graphtype[, c("indegree", "outdegree", "age") := lapply(.SD, round, 2), .SDcols = c("indegree", "outdegree", "age") ]
means_by_graphtype[, is_public := round(100*is_public, 2)]
temp <- rbind(dcast(means_by_graphtype, industrysection ~ type, value.var = "indegree"), dcast(means_by_graphtype, industrysection ~ type, value.var = "outdegree"))
temp <- rbind(temp, dcast(means_by_graphtype, industrysection ~ type, value.var = "age"))
temp <- rbind(temp, dcast(means_by_graphtype, industrysection ~ type, value.var = "is_public"))
temp$industrysection <- c("Average indegree", "Average outdegree", "Entity age", "Public limited company")
names(temp)[2:ncol(temp)] <- paste0("percent_", names(temp)[2:ncol(temp)])
means_by_graphtype <- temp
means_universe <- uk_basic_companies_data[, lapply(.SD, mean, na.rm = T), .SDcols = c("indegree", "outdegree", "age", "is_public")]
means_universe[, industrysection := "tempname" ]
means_universe[, c("indegree", "outdegree", "age") := lapply(.SD, round, 2), .SDcols = c("indegree", "outdegree", "age") ]
means_universe[, is_public := round(100*is_public, 2)]
temp <- rbind(dcast(means_universe, industrysection ~ ., value.var = "indegree"), dcast(means_universe, industrysection ~ ., value.var = "outdegree"))
temp <- rbind(temp, dcast(means_universe, industrysection ~ ., value.var = "age"))
temp <- rbind(temp, dcast(means_universe, industrysection ~ ., value.var = "is_public"))
temp$industrysection <- c("Average indegree", "Average outdegree", "Entity age", "Public limited company")
setnames(temp, ".", "percent_universe")
means_universe <- temp
means_validation <- graph_membership[ in_validation == 1, lapply(.SD, mean, na.rm = T), .SDcols = c("indegree", "outdegree", "age", "is_public")]
means_validation[, industrysection := "tempname" ]
means_validation[, c("indegree", "outdegree", "age") := lapply(.SD, round, 2), .SDcols = c("indegree", "outdegree", "age") ]
means_validation[, is_public := round(100*is_public, 2)]
temp <- rbind(dcast(means_validation, industrysection ~ ., value.var = "indegree"), dcast(means_validation, industrysection ~ ., value.var = "outdegree"))
temp <- rbind(temp, dcast(means_validation, industrysection ~ ., value.var = "age"))
temp <- rbind(temp, dcast(means_validation, industrysection ~ ., value.var = "is_public"))
temp$industrysection <- c("Average indegree", "Average outdegree", "Entity age", "Public limited company")
setnames(temp, ".", "percent_validation")
means_validation <- temp
# Long per industry data to wide summary table
summary_table <- dcast(industry_by_graphtype, industrysection ~ type, value.var = c("N", "percent"), fill = 0)
# Add the data on universe
summary_table <- merge(summary_table, industry_universe, by = "industrysection", all = T)
summary_table[ is.na(N_universe) & industrysection != "Individual", N_universe := 0]
summary_table[ is.na(percent_universe) & industrysection != "Individual", percent_universe := 0]
# Add the data on validation set
summary_table <- merge(summary_table, industry_validation, by = "industrysection", all = T)
summary_table[ is.na(N_validation) & industrysection != "Individual", N_validation := 0]
summary_table[ is.na(percent_validation) & industrysection != "Individual", percent_validation := 0]
# Proper order, so that total goes first
setorderv(summary_table, "percent_universe", -1)
# Add the data on degree and other variables to the bottom of the table
summary_table <- rbind(summary_table, means_by_graphtype, fill = T)
summary_table <- rbind(summary_table, means_universe, fill = T)
summary_table <- rbind(summary_table, means_validation, fill = T)
# Export to .tex table for future editing
#stargazer(summary_table, type = "latex", summary = F, out = "output/alphaicon_paper/summary_stat_by_type.tex", float = F, multicolumn = T, digits = 2)

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# This code plots the selected sub-networks
# in the PSC data and produces the figures
# for the α-ICON paper
library(data.table)
library(igraph)
library(stringi)
library(stringr)
library(ggplot2)
library(ggnetwork)
library(ggthemes)
library(showtext)
# Add the font to use
font_add_google("Open Sans", "Open Sans")
showtext_auto()
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Load the active participants snapshot of PSC (prepared by data_preparation/uk/2_psc_snapshot_to_participants_panel.r)
psc <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
# Load the companies data (prepared by data_preparation/uk/1b_process_companies_data.r)
load("data/uk/uk_basic_companies_data_2021-08-01.rdata")
# Load the transitive ownership of each participant at alpha = 0.999
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
holders <- fread("output/uk/transitive/uk_organisations_transitive_ownership_alpha0.999_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", colClasses = c("character", "character", "numeric"))
# Load the data on graph membership
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
graph_membership <- fread("output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", header = T, colClasses = c("numeric", "character", "factor"))
graph_membership[, V1 := NULL ]
setnames(graph_membership, "company_number/id", "participant_id")
gc()
# We need to pick up an illustrative organization
# Ideally this organization should have a small network size
# and have at least one entity in graph core
# Orgs in the core with all other types in the subgraph
# and manageable network size
temp <- holders[ participant_id %in% graph_membership[ type == "C"]$participant_id ]
temp[, company_type := graph_membership[ match(temp$company_number, graph_membership$participant_id) ]$type ]
temp[, participant_type := graph_membership[ match(temp$participant_id, graph_membership$participant_id) ]$type ]
# Devise a set of candidate orgs for illustration
# where all organization types are present in the company network
candidate_orgs <- temp[, list( company_types = uniqueN(company_type), network_size = uniqueN(company_number)), by = "participant_id"]
# Consider moderately sized networks with all types of orgs there
candidate_ids <- unique(candidate_orgs[ company_types > 2 & network_size <= 30 & network_size > 10]$participant_id)
# Additionally, consider the largest structure in terms
# of graph path from participant to company
# This is the result of igraph::farthest_vertices
# applied to the psc graph
farthest_components <- c("11443992")
# Also consider participant SEAN DINNEN
# he has DPI and NPI of 0 but very large transitivity score
sean_dinnen <- "SEAN$MICHAEL$DINNEN$1968$3"
# Example of long path
heidelbergcement <- "HEIDELBERGCEMENT AG$GERMANY$HRB 33082"
# Finally, consider the organizations with large difference between
# the super-holder scores (computed in alphaicon_paper/6_rank_top_holders.r)
top100_holders_diff_npi_dpi <- fread("output/alphaicon_paper/uk_organisations_top100_holders_diff_npi_dpi_2021_long_2aug21.csv", encoding = "UTF-8")
top100_holders_diff_transitive_dpi <- fread("output/alphaicon_paper/uk_organisations_top100_holders_diff_transitive_dpi_2021_long_2aug21.csv", encoding = "UTF-8")
top100_holders_diff_transitive_npi <- fread("output/alphaicon_paper/uk_organisations_top100_holders_diff_transitive_npi_2021_long_2aug21.csv", encoding = "UTF-8")
# Define the candidates to consider (from affiliated_entities
# and other inspection)
organizations_of_interest <- unique(c("IHS MARKIT LTD$BERMUDA$48610", "06647317", "11594795", candidate_ids, farthest_components, sean_dinnen))
# Or specify one organization for the graph in the paper:
#organizations_of_interest <- "03782947" # OPUS
organizations_of_interest <- c(top100_holders_diff_transitive_dpi[1]$participant_id, # SPECSAVERS OPTICAL SUPERSTORES LTD
top100_holders_diff_npi_dpi[82]$participant_id, # LENDLEASE INTERNATIONAL PTY LIMITED
top100_holders_diff_transitive_dpi[99]$participant_id, # THE BERKELEY GROUP PLC
top100_holders_diff_transitive_npi[17]$participant_id) # BAJLINDER$KAUR$BOPARAN$1968$1. NB: her husband RANJIT$SINGH$BOPARAN$1966$8 has alpha-ICON sum 73
# Iterate over multiple graph candidates
for( org_interest in organizations_of_interest ) {
# Ultimate companies held by this organization
holders_subset_ultimate <- holders[ participant_id %in% org_interest ]
# Consider their total interest in all entities
holders_subset <- psc[ participant_id %in% unique(holders_subset_ultimate$company_number) | company_number %in% unique(holders_subset_ultimate$company_number) ]
holders_subset <- holders_subset[ !is.na(equity_share)]
setnames(holders_subset, "equity_share", "share")
# Network size
#uniqueN(holders_subset$company_number)
#uniqueN(holders_subset$participant_id)
# Add company and participant names and countries of origin
holders_subset[, company_name := uk_basic_companies_data[ match(holders_subset$company_number, uk_basic_companies_data$CompanyNumber)]$CompanyName ]
#holders_subset[, company_country := uk_basic_companies_data[ match(holders_subset$company_number, uk_basic_companies_data$CompanyNumber)]$CountryOfOrigin ]
holders_subset[, participant_name := uk_basic_companies_data[ match(holders_subset$participant_id, uk_basic_companies_data$CompanyNumber)]$CompanyName ]
#holders_subset[, participant_country := uk_basic_companies_data[ match(holders_subset$participant_id, uk_basic_companies_data$CompanyNumber)]$CountryOfOrigin ]
# Proper name handling for individuals: first name-surname
holders_subset[grepl("$", participant_id, fixed = T) & kind != "individual", participant_name := as.data.table(stri_split_fixed(participant_id, "$", n = 3, simplify = T)[,1])]
holders_subset[kind == "individual", participant_name := paste0(stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 1], " ", stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 3])]
#holders_subset[, company_country := gsub("United Kingdom", "UK", company_country) ]
#holders_subset[, participant_country := gsub("United Kingdom", "UK", participant_country) ]
# Are the names unique?
#uniqueN(holders_subset$company_name)
#uniqueN(holders_subset$participant_name)
# Add the graph types of organizations
holders_subset[, company_type := graph_membership[ match(holders_subset$company_number, graph_membership$participant_id) ]$type ]
holders_subset[, participant_type := graph_membership[ match(holders_subset$participant_id, graph_membership$participant_id) ]$type ]
holders_subset[, share_range := NA_character_ ]
holders_subset[ share == 87.5, share_range := "75-100%"]
holders_subset[ share == 62.5, share_range := "50-75%"]
holders_subset[ share == 37.5, share_range := "25-50%"]
## Total number of holdings
holdings_count <- holders_subset[, list(count_holdings_total = .N), by = "participant_name"]
## Total number of holders
holders_count <- holders_subset[, list(count_holders_total = .N), by = "company_name"]
# To igraph object
## Create an object with vertex metadata
vertex_metadata <- unique(rbind(unique(data.table( name = holders_subset$company_name, type = holders_subset$company_type)),
data.table( name = holders_subset$participant_name, type = holders_subset$participant_type)
), by = "name")
vertex_metadata <- merge(vertex_metadata, holdings_count, by.x = "name", by.y = "participant_name", all.x = T, all.y = F, sort = F)
vertex_metadata <- merge(vertex_metadata, holders_count, by.x = "name", by.y = "company_name", all.x = T, all.y = F, sort = F)
vertex_metadata[is.na(count_holdings_total), count_holdings_total := 0]
vertex_metadata[is.na(count_holders_total), count_holders_total := 0]
# NA to mock 0
vertex_metadata[count_holdings_total == 0, count_holdings_total := 1]
# Remove intermediaries with no holders
vertex_metadata <- vertex_metadata[ !(count_holders_total == 0 & type == "I") ]
## Convert to igraph
holders_example_graph <- graph_from_data_frame(holders_subset[participant_name %in% vertex_metadata$name & company_name %in% vertex_metadata$name, c("participant_name", "company_name", "share", "share_range")], directed = T, vertices = vertex_metadata)
# Line-wrap the name
V(holders_example_graph)$name_label <- str_wrap(V(holders_example_graph)$name, 15)
# Graph to ggnetwork
holders_example_net <- ggnetwork(holders_example_graph, layout = with_kk(), arrow.gap = 0.01)
# Empty name for certain types if network is large
if(nrow(holders_example_net) > 150) {
holders_example_net[!(holders_example_net$type %in% c("SH", "C") | holders_example_net$name %in% c("SPECSAVERS UK HOLDINGS LIMITED", "HANSON PACKED PRODUCTS LIMITED", "HOUSERATE LIMITED", "HANSON LIMITED", "HEIDELBERGCEMENT UK HOLDING LIMITED") ), "name_label"] <- ""
}
# Plot the graph
holders_example_plot <- ggplot(holders_example_net, aes(x = x, y = y, xend = xend, yend = yend)) +
geom_edges(color = "#ebecf0", arrow = arrow(angle = 45, length = unit(5, "pt"), type = "closed"), show.legend = F) +
geom_nodes(aes(color = type, size = log(count_holdings_total)), show.legend = T) +
{ if( org_interest %in% c("03782947", "PHILIP$AULD$MACTAGGART$1956$2", "BAJLINDER$KAUR$BOPARAN$1968$1")) geom_edgetext(aes(label = share_range), color = "grey25", size = 1.5) } +
geom_nodetext_repel(aes(label = name_label, color = type), fontface = "bold", size = 2, show.legend = F, point.padding = 5, max.overlaps = 300) +
#{ if(nrow(holders_example_net) > 150) geom_nodetext_repel(aes(color = type), label = "", fontface = "bold", size = 2, show.legend = F, point.padding = 5) } +
#{ if(nrow(holders_example_net) <= 150) geom_nodetext_repel(aes(label = name, color = type), fontface = "bold", size = 2, show.legend = F, point.padding = 5) } +
scale_size(guide = "none") +
scale_color_manual(name = "node type", labels = c("super-holder", "super-target", "intermediary", "core"), values = c("SH" = "#66c2a5", "ST" = "#8da0cb", "I" = "grey", "C" = "#fc8d62")) +
guides(color = guide_legend(override.aes = list(size = 5))) +
theme_blank() + theme(text = element_text(family = "Open Sans"), legend.position = "bottom", plot.margin = unit(c(0, 0, 0, 0), "cm"))
# Export to an image
graph_file_name <- gsub("[[:punct:]]", "", stri_split_fixed(org_interest, "$", simplify = T)[1,1])
if( org_interest %in% c("SEAN$MICHAEL$DINNEN$1968$3", "SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624") ) {
ggsave(paste0("output/alphaicon_paper/network_examples/uk_example ", graph_file_name, ".pdf"), height = 20, width = 20, scale = 1.2, device = cairo_pdf)
} else {
ggsave(paste0("output/alphaicon_paper/network_examples/uk_example ", graph_file_name, ".pdf"), height = 10, width = 10, device = cairo_pdf)
}
message(graph_file_name)
}
########
# Plot the graph with the core components only
core <- psc[ participant_id %in% unique(graph_membership[type == "C"]$participant_id) & company_number %in% unique(graph_membership[type == "C"]$participant_id) ]
core <- core[ !is.na(equity_share)]
setnames(core, "equity_share", "share")
# Add company and participant names and countries of origin
core[, company_name := uk_basic_companies_data[ match(core$company_number, uk_basic_companies_data$CompanyNumber)]$CompanyName ]
core[, participant_name := uk_basic_companies_data[ match(core$participant_id, uk_basic_companies_data$CompanyNumber)]$CompanyName ]
# Proper name handling for individuals: first name-surname
core[grepl("$", participant_id, fixed = T) & kind != "individual", participant_name := as.data.table(stri_split_fixed(participant_id, "$", n = 3, simplify = T)[,1])]
core[kind == "individual", participant_name := paste0(stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 1], " ", stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 3])]
# Add the graph types of organizations
core[, company_type := graph_membership[ match(core$company_number, graph_membership$participant_id) ]$type ]
core[, participant_type := graph_membership[ match(core$participant_id, graph_membership$participant_id) ]$type ]
core[, share_range := NA_character_ ]
core[ share == 87.5, share_range := "75-100%"]
core[ share == 62.5, share_range := "50-75%"]
core[ share == 37.5, share_range := "25-50%"]
# Add the total number of companies where core participants
## Total number of holdings
core_holdings <- holders[participant_id %in% graph_membership[type == "C"]$participant_id, list(count_holdings_total = .N), by = "participant_id"]
## Holdings in core
core_holdings <- merge(core_holdings, holders[participant_id %in% graph_membership[type == "C"]$participant_id & company_number %in% graph_membership[type == "C"]$participant_id, list(count_holdings_core = .N), by = "participant_id"], by = "participant_id", all = T)
# To igraph object
## Create an object with vertex metadata
vertex_metadata <- unique(rbind(unique(data.table(name = core$company_name, type = core$company_type, id = core$company_number)),
data.table( name = core$participant_name, type = core$participant_type, id = core$participant_id)
), by = "name")
# Add the counts of holdings
vertex_metadata <- merge(vertex_metadata, core_holdings, by.x = "id", by.y = "participant_id", all = T)
vertex_metadata[, id := NULL]
# Keep only non-trivial components
vertex_metadata <- vertex_metadata[ count_holdings_core > 2 ]
## Convert to igraph
core_graph <- graph_from_data_frame(core[ participant_name %in% vertex_metadata$name | company_name %in% vertex_metadata$name, c("participant_name", "company_name", "share", "share_range")], directed = T, vertices = vertex_metadata)
# Line-wrap the name
V(core_graph)$name_label <- str_wrap(V(core_graph)$name, 15)
# Graph to ggnetwork
core_net <- ggnetwork(core_graph, layout = with_fr(), arrow.gap = 0.01)
# Plot the graph
core_plot <- ggplot(core_net, aes(x = x, y = y, xend = xend, yend = yend)) +
geom_edges(color = "grey", arrow = arrow(angle = 45, length = unit(3, "pt"), type = "closed"), show.legend = F) +
geom_nodes(aes(color = type, size = count_holdings_total), show.legend = T) +
geom_edgetext(aes(label = share_range), color = "grey25", size = 1) +
geom_nodetext_repel(aes(label = name_label, color = type), fontface = "bold", size = 2, show.legend = F, point.padding = 5) +
scale_size(guide = "none") +
scale_color_manual(name = "node type", labels = c("super-holder", "super-target", "intermediary", "core"), values = c("SH" = "#66c2a5", "ST" = "#8da0cb", "I" = "grey", "C" = "#fc8d62")) +
guides(color = guide_legend(override.aes = list(size = 5))) +
theme_blank() + theme(text = element_text(family = "Open Sans"), legend.position = "none", plot.margin = unit(c(0, 0, 0, 0), "cm"))
ggsave(paste0("output/network_examples/core_plot.pdf"), height = 10, width = 10, scale = 1.1, device = cairo_pdf)

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# This code evaluates various algorithms
# for ultimate owner identification
library(data.table)
library(stringi)
library(stringr)
library(igraph)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
############
# Load and prepare the data
# Load the active participants snapshot of PSC (prepared by data_preparation/uk/2_psc_snapshot_to_participants_panel.r)
psc <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
# Load the DPI of each participant after 10000 iterations (computed by alphaicon_paper/2_compute_npi_dpi.r)
holders_dpi <- fread("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
setnames(holders_dpi, c("entity", "participant", "dpi"), c("company_number", "participant_id", "share"))
holders_dpi[, times_pivotal := NULL ]
# Load the NPI of each participant after 10000 iterations (computed by alphaicon_paper/2_compute_npi_dpi.r)
holders_npi <- fread("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
setnames(holders_npi, c("entity", "participant", "npi"), c("company_number", "participant_id", "share"))
holders_npi[, times_pivotal := NULL ]
# Load the transitive ownership data at various alpha
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
alphas <- c("0.0", "0.1", "0.2", "0.3", "0.4", "0.5", "0.6", "0.7", "0.8", "0.9", "0.999")
for( a in alphas) {
# Transitive ownership on equity shares
temp1 <- fread(paste0("output/uk/transitive/uk_organisations_transitive_ownership_alpha", a, "_2021_long_2aug21.csv"), integer64 = "character", na.strings = "", encoding = "UTF-8", colClasses = c("character", "character", "numeric"))
assign(paste0("holders_transitive_alpha", a), temp1)
# Transitive ownership on DPI weights
temp2 <- fread(paste0("output/uk/transitive/uk_organisations_transitive_ownership_alpha", a, "_2021_long_7sep21_dpi_10000iter.csv"), integer64 = "character", na.strings = "", encoding = "UTF-8", colClasses = c("character", "character", "numeric"))
assign(paste0("holders_transitivedpi_alpha", a), temp2)
rm(temp1); rm(temp2)
}
# Load the data on graph membership
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
graph_membership <- fread("output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", header = T, colClasses = c("numeric", "character", "factor"))
graph_membership[, V1 := NULL ]
setnames(graph_membership, "company_number/id", "participant_id")
# Load the data for evaluation of the algorithms (prepared by data_preparation/uk/3_prepare_affiliated_entities_evaluation_data.r)
affiliated_entities <- fread("data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
# Remove the CorpWatch entity identifiers
affiliated_entities[, c("subsidiary_cw_id", "parent_cw_id") := NULL ]
# Add the data on the shortest paths from parent to subsidiary
psc_graph <- graph_from_data_frame(psc[participant_id != company_number & !is.na(equity_share), c("participant_id", "company_number", "equity_share"), with = F], directed = T)
# Compute all the distances on the graph
# from parent companies in the gold standard
# data to the subsidiates
affiliated_distance_mat <- distances(psc_graph, v = which(V(psc_graph)$name %in% unique(affiliated_entities$participant_id)), to = which(V(psc_graph)$name %in% affiliated_entities$company_number), mode = "out")
# Arrange them so that the distance is on the main diagonal
affiliated_distance <- as.data.table(as.table(affiliated_distance_mat))
names(affiliated_distance) <- c("participant_id", "company_number", "path_length")
# Remove non-reachable entries
affiliated_distance <- affiliated_distance[ is.finite(path_length) ]
# Add the path lengths to the affiliated entities data
affiliated_entities <- merge(affiliated_entities, affiliated_distance, by = c("company_number", "participant_id"), all.x = T, all.y = F, sort = F)
#affiliated_entities[, .N, by = "path_length"]
#nrow(affiliated_entities[!is.na(path_length)] # 1007
# Keep only affiliated entities reachable on the PSC graph
affiliated_entities <- affiliated_entities[ !is.na(path_length) ]
# List all holder objects that are loaded in the memory
holder_objects <- paste0("holders_", c("dpi", "npi", paste0("transitive_alpha", alphas), paste0("transitivedpi_alpha", alphas)))
############
# Subset holder objects
# Keep only the affiliated entities in the holder objects (to speed up the computation time)
for(obj in holder_objects) {
assign(obj, get(obj)[ company_number %in% affiliated_entities$company_number | company_number %in% affiliated_entities$participant_id | participant_id %in% affiliated_entities$company_number | participant_id %in% affiliated_entities$participant_id])
# Add the entity type for objects
assign(obj, merge(get(obj), graph_membership, by = "participant_id", all.x = T, all.y = F, sort = F))
}
# Add the ranks
for(obj in holder_objects) {
# Sort by descending share within companies
setorderv(get(obj), c("company_number", "share"), c(1, -1))
# Add the rank
get(obj)[, rank := 1:.N, by = "company_number"]
# Devise another rank
# that ranks participants within types
get(obj)[, rankbygraphtype := 1:.N, by = c("company_number", "type")]
}
# Debug: holders_transitive_alpha0.5[company_number == "SL033942"]
# Create a single object with ranks under different algorithms
algorithms <- c("dpi", "npi", paste0("transitive_alpha", alphas), paste0("transitivedpi_alpha", alphas))
# Start with the actual participants data (for the baseline algorithm)
holders_algorithm_ranks <- psc[ company_number %in% affiliated_entities$company_number, c("company_number", "participant_id", "equity_share"), with = F]
holders_algorithm_ranks <- holders_algorithm_ranks[ !is.na(equity_share) ]
# For the baseline algorithm simply take the equity share
setorderv(holders_algorithm_ranks, c("company_number", "equity_share"), c(1, -1))
holders_algorithm_ranks[, rank_baseline := 1:.N, by = "company_number" ]
holders_algorithm_ranks[, equity_share := NULL ]
# For the remaining ranks query the holders object
for(alg in algorithms) {
cols_to_keep <- intersect(names(get(paste0("holders_", alg))), c("company_number", "participant_id", "rank", "rankbygraphtype"))
holders_algorithm_ranks <- merge(holders_algorithm_ranks, get(paste0("holders_", alg))[, c(cols_to_keep), with = F], by = c("company_number", "participant_id"), all.x = T, all.y = T, sort = F)
setnames(holders_algorithm_ranks, "rank", paste0("rank_", alg))
setnames(holders_algorithm_ranks, "rankbygraphtype", paste0("rankbygraphtype_", alg), skip_absent = T)
message(alg)
}
# Add the participant type in graph
holders_algorithm_ranks[, type := graph_membership[ match(holders_algorithm_ranks$participant_id, graph_membership$participant_id)]$type ]
# What rank do the actual super-holders from the affiliated entities evaluation data
# take under each algorithm
holders_algorithm_ranks_affiliated <- holders_algorithm_ranks[ company_number %in% affiliated_entities$company_number]
# Add the ground truth participant id
holders_algorithm_ranks_affiliated <- merge(holders_algorithm_ranks_affiliated, affiliated_entities[, -"path_length"], by = c("company_number"), all = T, sort = F)
# NB: We have duplicates:
# holders_algorithm_ranks_affiliated[ company_number == "00906355"]
# Debug:
#holders_algorithm_ranks[ company_number == "00027883"]
#holders_algorithm_ranks_affiliated[ company_number == "00027883"]
# Add the path lengths to the data
holders_algorithm_ranks_affiliated <- merge(holders_algorithm_ranks_affiliated, affiliated_entities, by.x = c("company_number", "participant_id.y"), by.y = c("company_number", "participant_id"), sort = F, all.x = T, all.y = F)
# What rank does the truth take under each algorithm
algorithms <- unique(c("baseline", algorithms))
for(alg in algorithms) {
holders_algorithm_ranks_affiliated[, paste0("rank_true_", alg) := NA_real_ ]
holders_algorithm_ranks_affiliated[participant_id.x == participant_id.y, paste0("rank_true_", alg) := get(paste0("rank_", alg)) ]
# Add the rank when we consider only super-holders
if( !grepl("baseline", alg) ) {
holders_algorithm_ranks_affiliated[ participant_id.x == participant_id.y & type == "SH", paste0("rankonlysuperholder_true_", alg) := get(paste0("rankbygraphtype_", alg))]
# Restore the original value if no rank for super-holder
holders_algorithm_ranks_affiliated[ is.na(get(paste0("rankonlysuperholder_true_", alg))) , paste0("rankonlysuperholder_true_", alg) := get(paste0("rank_true_", alg)) ]
}
}
# Aggregate at company level
cols_of_interest <- names(holders_algorithm_ranks_affiliated)[ grepl("rank.*_true_", names(holders_algorithm_ranks_affiliated))]
cols_of_interest <- c(cols_of_interest, "path_length")
affiliated_evaluation_results <- holders_algorithm_ranks_affiliated[, lapply(.SD, min, na.rm = T), .SDcols = cols_of_interest, by = "company_number"]
affiliated_evaluation_results[, c(cols_of_interest) := lapply(.SD, function(x) ifelse(is.finite(x), x, NA)), .SDcols = cols_of_interest]
# With the above min-aggregation we resolve the issue with duplicates
# affiliated_evaluation_results[ company_number == "00906355"]
# Compute recall @ different k for algorithms
## Init an object to store the recall
algorithm_recall <- data.table()
## Init an object to store the recall at different path lengths
algorithm_recall_by_pathlength <- data.table()
path_lengths <- unique(holders_algorithm_ranks_affiliated$path_length)
path_lengths <- path_lengths[ order(path_lengths) ]
path_lengths <- path_lengths[ !is.na(path_lengths) ]
for(k in 1:10) {
for( alg in algorithms ) {
# How many organisations have the true participant out of all k participants
recall <- nrow(affiliated_evaluation_results[ get(paste0("rank_true_", alg)) <= k ])/nrow(affiliated_evaluation_results)
algorithm_recall <- rbind(algorithm_recall, data.table(algorithm = alg, k = k, superholderpriority = 0, recall = recall), fill = T)
# Special recall considering only super-holders
if( !grepl("baseline", alg) ) {
recallsh <- nrow(affiliated_evaluation_results[ get(paste0("rankonlysuperholder_true_", alg)) <= k ])/nrow(affiliated_evaluation_results)
algorithm_recall <- rbind(algorithm_recall, data.table(algorithm = alg, k = k, superholderpriority = 1, recall = recallsh), fill = T)
}
# Same for each path lengths
for( p in path_lengths ) {
recallpath <- nrow(affiliated_evaluation_results[ get(paste0("rank_true_", alg)) <= k & path_length == p ])/nrow(affiliated_evaluation_results[ path_length == p | is.na(path_length) ])
algorithm_recall_by_pathlength <- rbind(algorithm_recall_by_pathlength, data.table(algorithm = alg, k = k, superholderpriority = 0, path = p, recall = recallpath), fill = T)
if( !grepl("baseline", alg) ) {
recallpathsh <- nrow(affiliated_evaluation_results[ get(paste0("rankonlysuperholder_true_", alg)) <= k & path_length == p ])/nrow(affiliated_evaluation_results[ path_length == p | is.na(path_length) ] )
algorithm_recall_by_pathlength <- rbind(algorithm_recall_by_pathlength, data.table(algorithm = alg, k = k, superholderpriority = 1, path = p, recall = recallpathsh), fill = T)
}
}
}
}
# Save point
fwrite(algorithm_recall, file = "output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall.csv")
fwrite(algorithm_recall_by_pathlength, file = "output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall_by_pathlength.csv")
# Manual inspection for tables
#algorithm_recall[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 ]
#algorithm_recall[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 3 ]
#algorithm_recall[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 5 ]
#algorithm_recall[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 10 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 1 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 2 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 3 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 4 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 5 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 10 ]
#algorithm_recall_by_pathlength[ algorithm %in% c("baseline", "dpi", "npi", "transitive_alpha0.0", "transitive_alpha0.999", "transitivedpi_alpha0.999") & k == 1 & path == 12 ]
############
# Plot the results
library(data.table)
library(ggplot2)
library(ggthemes)
library(ggrepel)
library(stringi)
library(showtext)
setwd(Sys.getenv('ALPHAICON_PATH'))
# Add the font to use
font_add_google("Open Sans", "Open Sans")
showtext_auto()
# Load the files with evaluation results
algorithm_recall <- fread("output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall.csv", encoding = "UTF-8")
algorithm_recall_by_pathlength <- fread("output/alphaicon_paper/uk_orgs_algorithm_evaluation_recall_by_pathlength.csv", encoding = "UTF-8")
for(obj in c("algorithm_recall", "algorithm_recall_by_pathlength") ) {
# Column marking whether we use DPI weights
get(obj)[, dpi_weights := 0]
get(obj)[grepl("dpi", algorithm, ignore.case = T), dpi_weights := 1]
# Shorter names
get(obj)[, algorithm := gsub("transitive.*_alpha", "α=", algorithm)]
get(obj)[, algorithm := gsub("transitivedpi_alpha", "α=", algorithm)]
# Extract alpha values from the name
get(obj)[, alpha := as.numeric(stri_split_fixed(algorithm, "α=", n = 2, simplify = T)[,2]) ]
# Add the superholder mark to corresponding algorithm names
get(obj)[ superholderpriority == 1, algorithm := paste0(algorithm, " SH")]
# Add the DPI weight mark to corresponding algorithm names
get(obj)[ dpi_weights == 1 & grepl("α", algorithm), algorithm := paste0(algorithm, " DPI")]
# Certain names to upper case
get(obj)[, algorithm := gsub("dpi", "DPI", algorithm) ]
get(obj)[, algorithm := gsub("npi", "NPI", algorithm) ]
}
########
# Produce the evaluation plots (overall)
# One subset for display: only the best performing α-ICON versus other algorithms
algorithm_recall_otheralgs <- algorithm_recall[ algorithm %in% c("DPI", "NPI", "α=0.999", "α=0.999 SH")]
## Other algorithms vs best and worst-performing α-ICON algorithm
recall_plot <- ggplot(aes(x = k, y = recall, group = algorithm, color = algorithm), data = algorithm_recall_otheralgs) +
geom_line(size = 1.5, alpha = 1) +
geom_point(size = 2) +
scale_x_continuous(breaks = 1:10) +
geom_text(aes(label = algorithm, colour = algorithm, x = k-1, y = recall), data = algorithm_recall_otheralgs[k == 1 & algorithm == "DPI"], size = 8, hjust = 0.3) +
geom_text(aes(label = algorithm, colour = algorithm, x = k-1, y = recall), data = algorithm_recall_otheralgs[k == 1 & algorithm == "α=0.999"], size = 8, hjust = 0.7) +
geom_text(aes(label = algorithm, colour = algorithm, x = k-1, y = recall), data = algorithm_recall_otheralgs[k == 1 & algorithm == "NPI"], size = 8, hjust = 0.3) +
geom_text(aes(label = algorithm, colour = algorithm, x = k-1, y = recall), data = algorithm_recall_otheralgs[k == 1 & algorithm == "α=0.999 SH"], size = 8, hjust = 0.5, vjust = -0.6) +
#geom_text_repel(aes(label = algorithm, colour = algorithm, x = k-1, y = recall), data = algorithm_recall_otheralgs[k == 1], size = 8, hjust = 0.5) +
labs(y = expression("Recall @ "~italic("k")), x = expression(italic("k"))) +
#scale_colour_brewer(type = "qual", palette = 2) +
scale_color_manual(name = "", values = c("#b2df8a", "#33a02c", "#a6cee3", "#1f78b4")) +
expand_limits(x = c(-1.5, 10)) +
theme_minimal() + theme(legend.position = "none", text = element_text(size = 18, family = "Open Sans"), panel.grid.major = element_blank(), panel.grid.minor = element_blank())
ggsave(recall_plot, file = "output/alphaicon_paper/recall_plot.pdf", width = 12, height = 9, device = cairo_pdf, scale = 0.6)
# Another subset for display: only α-ICON under different alphas
algorithm_recall_onlyalphas <- algorithm_recall[ alpha > 0 & superholderpriority == 1 & dpi_weights == 0]
# Group the duplicated values of recall at alphas
alpha_group <- algorithm_recall_onlyalphas[ k == 1, list(alphagroup = .GRP), by = "recall"]
alpha_group <- merge(alpha_group, algorithm_recall_onlyalphas[ k == 1, c("alpha", "recall")], by = "recall")
alpha_group[, recall := NULL]
# Generate the label text for alpha group
alpha_group[, minalpha := min(alpha), by = "alphagroup"]
alpha_group[, maxalpha := max(alpha), by = "alphagroup"]
alpha_group[ minalpha == maxalpha, alphagrouplabel := as.character(round(alpha, 1))]
alpha_group[ minalpha != maxalpha, alphagrouplabel := as.character(paste0(round(minalpha, 1), "-", round(maxalpha, 3)))]
alpha_group[, alphagrouplabel := paste0("α=", alphagrouplabel)]
algorithm_recall_onlyalphas[, alphagroup := alpha_group[match(algorithm_recall_onlyalphas$alpha, alpha_group$alpha)]$alphagrouplabel]
# Make alpha groups unique
algorithm_recall_onlyalphas <- unique(algorithm_recall_onlyalphas, by = c("alphagroup", "k"))
## Other algorithms vs best and worst-performing transitive algorithm
recall_plot_alphas <- ggplot(aes(x = k, y = recall, group = alphagroup, color = as.factor(alpha)), data = unique(algorithm_recall_onlyalphas)) +
geom_line(size = 1.5, alpha = 1) +
geom_point(size = 2) +
scale_x_continuous(breaks = 1:10) +
geom_text(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 4 & alpha == 0.1 ], hjust = 0.3) +
geom_text(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 2 & alpha == 0.5 ], vjust = -4, hjust = 0.1) +
geom_text(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 3 & alpha == 0.7 ], hjust = -0.1) +
geom_text(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 1 & alpha == 0.8 ], vjust = 1, hjust = -0.1) +
geom_text(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 2 & alpha == 0.9 ], hjust = 0.4) +
#geom_text_repel(aes(label = alphagroup, colour = as.factor(alpha), group = alphagroup, x = k-2.5, y = recall), size = 8, data = algorithm_recall_onlyalphas[k == 1], hjust = 0, min.segment.length = 10) +
scale_colour_brewer(type = "qual", palette = 2) +
labs(y = expression("Recall @ "~italic("k")), x = expression(italic("k"))) +
expand_limits(x = c(-2, 10)) +
theme_minimal() + theme(legend.position = "none", text = element_text(size = 18, family = "Open Sans"), panel.grid.major = element_blank(), panel.grid.minor = element_blank())
ggsave(recall_plot_alphas, file = "output/alphaicon_paper/recall_plot_alphas.pdf", width = 12, height = 9, device = cairo_pdf, scale = 0.6)
# For reporting: table with recall
algorithms_to_report <- c("baseline", "DPI", "NPI", "NPI SH", "α=0.0", "α=0.999", "α=0.999 SH", "α=0.999 SH DPI")
algorithm_recall[, recall := round(recall, 3) ]
algorithm_recall[ k == 1 & algorithm %in% algorithms_to_report, c("algorithm", "recall")]
algorithm_recall[ k == 3 & algorithm %in% algorithms_to_report, c("algorithm", "recall")]
algorithm_recall[ k == 5 & algorithm %in% algorithms_to_report, c("algorithm", "recall")]
algorithm_recall[ k == 10 & algorithm %in% algorithms_to_report, c("algorithm", "recall")]
########
# Produce the evaluation plots (by path length)
# One subset for display: only the best performing α-ICON versus other algorithms
algorithm_recall_by_pathlength_otheralgs <- algorithm_recall_by_pathlength[ algorithm %in% c("NPI", "α=0.999", "α=0.999 SH") ]
## Other algorithms vs best and worst-performing α-ICON algorithm
recall_path_plot <- ggplot(aes(x = path, y = recall, group = algorithm, color = algorithm), data = algorithm_recall_by_pathlength_otheralgs[ k == 1 ]) +
geom_line(size = 1.5, alpha = 1) +
geom_point(size = 2) +
scale_x_continuous(breaks = 1:12) +
scale_y_continuous(limits = c(0, 1)) +
labs(y = "Recall @ 1 for parents within path", x = expression(italic("l")~", path length from subsidiary to parent")) +
#scale_colour_brewer(type = "qual", palette = 3) +
scale_color_manual(name = "", values = c("#b2df8a", "#33a02c", "#1f78b4")) +
expand_limits(x = c(1, 12)) +
theme_minimal() + theme(legend.position = "bottom", text = element_text(size = 18, family = "Open Sans"), panel.grid.major = element_blank(), panel.grid.minor = element_blank())
ggsave(recall_path_plot, file = "output/alphaicon_paper/recall_path_plot_at_1.pdf", width = 12, height = 9, device = cairo_pdf, scale = 0.6)
# For reporting: table with recall
algorithm_recall_by_pathlength[, recall := round(recall, 3) ]
algorithms_path_length_to_report <- c("baseline", "DPI", "NPI", "NPI SH", "α=0.0", "α=0.999", "α=0.999 SH", "α=0.999 SH DPI")
algorithm_recall_by_pathlength[ path == 1 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 2 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 3 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 4 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 5 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 10 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]
algorithm_recall_by_pathlength[ path == 12 & algorithm %in% algorithms_path_length_to_report & k == 1, c("algorithm", "recall") ]

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# This code sums the computed control shares
# of the super-holders in the PSC data and
# produces the rankings under different algorithms
# for the α-ICON paper
library(data.table)
library(lubridate)
library(stringi)
library(stringr)
library(stargazer)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
############
# Data loading
# Load the active participants snapshot of PSC (prepared by data_preparation/uk/2_psc_snapshot_to_participants_panel.r)
psc <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
# Load the companies data (prepared by data_preparation/uk/1b_process_companies_data.r)
load("data/uk/uk_basic_companies_data_2021-08-01.rdata")
# Load the DPI of each participant after 10000 iterations (computed by alphaicon_paper/2_compute_npi_dpi.r)
holders_dpi <- fread("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_dpi_10000iter.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
setnames(holders_dpi, c("entity", "participant", "dpi"), c("company_number", "participant_id", "share"))
holders_dpi[, times_pivotal := NULL ]
# Load the NPI of each participant after 10000 iterations (computed by alphaicon_paper/2_compute_npi_dpi.r)
holders_npi <- fread("output/uk/npi_dpi/10000iter/uk_organisations_participants_2021_long_7sep21_npi_10000iter.csv", integer64 = "character", na.strings = "", encoding = "UTF-8")
setnames(holders_npi, c("entity", "participant", "npi"), c("company_number", "participant_id", "share"))
holders_npi[, times_pivotal := NULL ]
# Load the transitive ownership data at various alpha
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
alphas <- c("0.0", "0.1", "0.2", "0.3", "0.4", "0.5", "0.6", "0.7", "0.8", "0.9", "0.999")
for( a in alphas) {
temp <- fread(paste0("output/uk/transitive/uk_organisations_transitive_ownership_alpha", a, "_2021_long_2aug21.csv"), integer64 = "character", na.strings = "", encoding = "UTF-8", colClasses = c("character", "character", "numeric"))
assign(paste0("holders_transitive_alpha", a), temp)
rm(temp)
}
# Load the data on graph membership
# (prepared by alphaicon_paper/1_compute_alphaicon.ipynb)
graph_membership <- fread("output/uk/uk_organisations_participation_graph_core_periphery_membership_6aug21.csv", integer64 = "character", na.strings = "", encoding = "UTF-8", header = T, colClasses = c("numeric", "character", "factor"))
graph_membership[, V1 := NULL ]
setnames(graph_membership, "company_number/id", "participant_id")
# All holder objects that are loaded in the memory
holder_objects <- paste0("holders_", c("dpi", "npi", paste0("transitive_alpha", alphas)))
# Add the graph membership and remove self-loops
for(obj in holder_objects) {
get(obj)[, participant_type := graph_membership[ match(get(obj)$participant_id, graph_membership$participant_id) ]$type ]
get(obj)[, company_type := graph_membership[ match(get(obj)$company_number, graph_membership$participant_id) ]$type ]
assign(obj, get(obj)[ company_number != participant_id ])
}
psc[, participant_type := graph_membership[ match(psc$participant_id, graph_membership$participant_id) ]$type ]
psc[, company_type := graph_membership[ match(psc$company_number, graph_membership$participant_id) ]$type ]
############
# Identify top holders
# Compute total holdings (weighted and unweighted by assets)
holdings_dpi <- holders_dpi[, list( sumdpi = sum(share)), by = "participant_id"]
holdings_dpi[, rankdpi := frankv(sumdpi, order = -1, ties.method = "first")]
holdings_npi <- holders_npi[, list( sumnpi = sum(share)), by = "participant_id"]
holdings_npi[, ranknpi := frankv(sumnpi, order = -1, ties.method = "first")]
# Normalize shares by type to one for our transitive data
holders_transitive_alpha0.999[, share_typenormalized := share/sum(share), by = c("company_number", "participant_type")]
# Keep only super-holders and sum up their shares
holdings_transitive <- holders_transitive_alpha0.999[participant_type == "SH", list( sumtransitive = sum(share_typenormalized)), by = "participant_id"]
# Rank the holders by their share
holdings_transitive[, ranktransitive := frankv(sumtransitive, order = -1, ties.method = "first")]
# Top-100 participants by our metric compared to other metrics
top_holders <- setorderv(holdings_transitive, "ranktransitive", 1)[1:100]
# Add ranks from other algorithms
top_holders <- merge(top_holders, holdings_dpi, by = "participant_id", all.x = T, all.y = F, sort = F)
top_holders <- merge(top_holders, holdings_npi, by = "participant_id", all.x = T, all.y = F, sort = F)
# Proper names
## First, match on company number with companies data
top_holders[, participant_name := uk_basic_companies_data[ match(top_holders$participant_id, uk_basic_companies_data$CompanyNumber)]$CompanyName ]
## Second, extract the company name
top_holders[ str_count(participant_id, fixed("$")) == 2, participant_name := stri_split_fixed(participant_id, "$", n = 3, simplify = T)[,1] ]
## Third, add the first and last names of the persons
top_holders[ str_count(participant_id, fixed("$")) == 4, participant_name := paste0(stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 1], " ", stri_split_fixed(participant_id, "$", n = 4, simplify = T)[, 3]) ]
## We no longer need participant id
#top_holders[, participant_id := NULL ]
# Proper column order
setcolorder(top_holders, c("participant_name", "participant_id", "ranktransitive", "ranknpi", "rankdpi", "sumtransitive", "sumnpi", "sumdpi"))
# Round the score
top_holders[, c("sumtransitive", "sumnpi", "sumdpi") := lapply(.SD, round, 1), .SDcols = c("sumtransitive", "sumnpi", "sumdpi") ]
# Add the size of the network of holdings and the core-shell distribution
top_holders_network_chars <- data.table()
for(superholder_id in top_holders$participant_id) {
# Debug: superholder_id <- "SC095000"
# Ultimate companies held by this organization
holders_subset_ultimate <- holders_transitive_alpha0.999[ participant_id %in% superholder_id ]
# Consider their total interest in all entities
holders_subset <- psc[ participant_id %in% unique(holders_subset_ultimate$company_number) | company_number %in% unique(holders_subset_ultimate$company_number) ]
holders_subset <- holders_subset[ !is.na(equity_share)]
holders_subset <- holders_subset[ participant_id != company_number]
# Share to 0-1 range
setnames(holders_subset, "equity_share", "share")
holders_subset[, share := share/100]
## Create an object with vertex metadata
vertex_metadata <- unique(rbind(unique(data.table( name = holders_subset$company_number, type = holders_subset$company_type)),
data.table( name = holders_subset$participant_id, type = holders_subset$participant_type)
), by = "name")
# Count all vertex types
out <- vertex_metadata[, .N, by = "type"]
# Transpose
out <- dcast(melt(out, id.vars = "type"), variable ~ type)
out[, variable := NULL ]
# Keep only the columns of interest in the order of interest
types_of_interest <- c("SH", "ST", "I", "C")
names_outside_types_of_interest <- types_of_interest[!(types_of_interest %in% names(out))]
if( length(names_outside_types_of_interest) > 0) {
out[, c(names_outside_types_of_interest) := 0]
}
out <- out[, types_of_interest, with = F]
# Add the network size
out <- data.table(participant_id = superholder_id, nodes = nrow(vertex_metadata), out)
top_holders_network_chars <- rbind(top_holders_network_chars, out, fill = T)
message(superholder_id)
}
# Add to the top holders data
top_holders <- merge(top_holders, top_holders_network_chars, by = "participant_id", sort = F)
# Write to CSV
fwrite(top_holders, file = "output/alphaicon_paper/uk_organisations_top100_holders_2021_long_2aug21.csv")
# Produce a TeX table
#stargazer(top_holders[1:25, -"participant_id"], type = "latex", summary = F, out = "output/alphaicon_paper/uk_organisations_top25_holders_2021_long_2aug21.tex", float = F, multicolumn = T, digits = 1)
# Export the information on top-25 entities with the largest deviation between ranks
combined_holdings <- merge(holdings_dpi, holdings_npi, by = "participant_id", all = T)
combined_holdings <- merge(combined_holdings, holdings_transitive, by = "participant_id", all = T)
combined_holdings[, diff_npi_dpi := sumnpi - sumdpi ]
combined_holdings[, diff_transitive_dpi := sumtransitive - sumdpi ]
combined_holdings[, diff_transitive_npi := sumtransitive - sumnpi ]
top100_holders_diff_npi_dpi <- setorderv(combined_holdings, "diff_npi_dpi", -1, na.last = T)[1:100]
top100_holders_diff_transitive_dpi <- setorderv(combined_holdings, "diff_transitive_dpi", -1, na.last = T)[1:100]
top100_holders_diff_transitive_npi <- setorderv(combined_holdings, "diff_transitive_npi", -1, na.last = T)[1:100]
# Export point
#fwrite(top100_holders_diff_npi_dpi, file = "output/alphaicon_paper/uk_organisations_top100_holders_diff_npi_dpi_2021_long_2aug21.csv")
#fwrite(top100_holders_diff_transitive_dpi, file = "output/alphaicon_paper/uk_organisations_top100_holders_diff_transitive_dpi_2021_long_2aug21.csv")
#fwrite(top100_holders_diff_transitive_npi, file = "output/alphaicon_paper/uk_organisations_top100_holders_diff_transitive_npi_2021_long_2aug21.csv")
############
# Agreement between rankings
# Add the ranks (takes time)
for(obj in holder_objects) {
# Create temporary variable prioritising super-holders
if( grepl("transitive", obj) ) {
get(obj)[, superholder := 0]
get(obj)[participant_type == "SH", superholder := 1]
}
# Sort by descending share within companies
if( grepl("transitive", obj) ) {
setorderv(get(obj), c("company_number", "superholder", "share"), c(1, -1, -1))
} else {
setorderv(get(obj), c("company_number", "share"), c(1, -1))
}
# Add the rank that prioritises super-holders
get(obj)[, rank := 1:.N, by = c("company_number")]
message(obj)
}
# Combine the ranks from all the methods
vars_to_keep <- c("company_number", "participant_id", "rank")
## DPI and NPI
holders_rankings <- merge(holders_dpi[, c(vars_to_keep), with = F], holders_npi[, c(vars_to_keep), with = F], by = c("company_number", "participant_id"), all = T)
setnames(holders_rankings, c("rank.x", "rank.y"), c("rank_dpi", "rank_npi"))
## Add transitive holder hankings (only super-holders or top-ranking non-super-holders)
for( a in alphas) {
holders_rankings <- merge(holders_rankings, get(paste0("holders_transitive_alpha", a))[ participant_type == "SH" | (participant_type != "SH" & rank == 1), c(vars_to_keep), with = F], by = c("company_number", "participant_id"), all = T)
setnames(holders_rankings, c("rank"), paste0("rank_transitive", a))
}
# Count holders by company from each method
holders_rankings[, countholders_dpi := sum(!is.na(rank_dpi)), by = "company_number"]
holders_rankings[, countholders_npi := sum(!is.na(rank_npi)), by = "company_number"]
for( a in alphas) {
holders_rankings[, paste0("countholders_transitive", a) := sum(!is.na(get(paste0("rank_transitive", a)))), by = "company_number"]
message(a)
}
# Pairs of counts of holders by company
holders_rankings[, countholders_dpi_npi := sum(!is.na(rank_dpi) & !is.na(rank_npi)), by = "company_number"]
for( a in alphas) {
holders_rankings[, paste0("countholders_dpi_transitive", a) := sum(!is.na(rank_dpi) & !is.na(get(paste0("rank_transitive", a)))), by = "company_number"]
holders_rankings[, paste0("countholders_npi_transitive", a) := sum(!is.na(rank_npi) & !is.na(get(paste0("rank_transitive", a)))), by = "company_number"]
message(a)
}
## Compute company-level Kendal's tau-b rank correlation coefficient
### (takes about 15 minutes per pair)
tau_dpi_npi <- holders_rankings[ countholders_dpi_npi > 1 & !is.na(rank_dpi) & !is.na(rank_npi), list(kendalltau_dpi_npi = cor(rank_dpi, rank_npi, method = "kendall", use = "pairwise.complete.obs")), by = "company_number"]
for( a in alphas) {
eval(parse(text = paste0("tau_dpi_transitive", a, " <- holders_rankings[ countholders_dpi_transitive", a, " > 1 & !is.na(rank_dpi) & !is.na(rank_transitive", a, "), list(kendalltau_dpi_transitive", a, " = cor(rank_dpi, rank_transitive", a, ", method = 'kendall', use = 'pairwise.complete.obs')), by = 'company_number']")))
eval(parse(text = paste0("tau_npi_transitive", a, " <- holders_rankings[ countholders_npi_transitive", a, " > 1 & !is.na(rank_npi) & !is.na(rank_transitive", a, "), list(kendalltau_npi_transitive", a, " = cor(rank_npi, rank_transitive", a, ", method = 'kendall', use = 'pairwise.complete.obs')), by = 'company_number']")))
message(a)
}
# Examples of companies with complex rankings
#holders_rankings[ company_number == "00026306"]
#holders_rankings[ company_number == "00000529"]
#holders_rankings[ company_number == "00018751"]
# Debug: these should be zeros
#holders_rankings[ countholders_dpi == 1 & countholders_npi == 1 & rank_dpi != rank_npi]
#holders_rankings[ countholders_transitive0.999 == 1 & countholders_npi == 1 & rank_transitive0.999 != rank_npi]
# Add the tau-b = 1 for companies with one participant (both direct and indirect)
tau_dpi_npi <- rbind(tau_dpi_npi, data.table(company_number = unique(holders_rankings[ countholders_dpi == 1 & countholders_npi == 1 & !is.na(rank_dpi) & !is.na(rank_npi) ]$company_number), kendalltau_dpi_npi = 1))
for( a in alphas) {
eval(parse(text = paste0("tau_dpi_transitive", a, " <- rbind(tau_dpi_transitive", a, ", data.table( company_number = unique(holders_rankings[ countholders_dpi == 1 & countholders_transitive", a, " == 1 & !is.na(rank_dpi) & !is.na(rank_transitive", a, ")]$company_number), kendalltau_dpi_transitive", a, " = 1))")))
eval(parse(text = paste0("tau_npi_transitive", a, " <- rbind(tau_npi_transitive", a, ", data.table( company_number = unique(holders_rankings[ countholders_npi == 1 & countholders_transitive", a, " == 1 & !is.na(rank_npi) & !is.na(rank_transitive", a, ")]$company_number), kendalltau_npi_transitive", a, " = 1))")))
}
# Add the tau-b = -1 for companies with differing number of participants
# where ranks do not match. Example: holders_rankings[ company_number == "00026306"]
tau_dpi_npi <- rbind(tau_dpi_npi, data.table(company_number = unique(holders_rankings[ !(company_number %in% tau_dpi_npi$company_number)]$company_number), kendalltau_dpi_npi = -1))
for( a in alphas) {
eval(parse(text = paste0("tau_dpi_transitive", a, " <- rbind(tau_dpi_transitive", a, ", data.table( company_number = unique(holders_rankings[ !(company_number %in% tau_dpi_transitive", a, "$company_number) ]$company_number), kendalltau_dpi_transitive", a, " = -1))")))
eval(parse(text = paste0("tau_npi_transitive", a, " <- rbind(tau_npi_transitive", a, ", data.table( company_number = unique(holders_rankings[ !(company_number %in% tau_npi_transitive", a, "$company_number) ]$company_number), kendalltau_npi_transitive", a, " = -1))")))
}
# Finally, we need to fill in NAs like tau_dpi_transitive0.999[company_number == "00001615"]
# holders_rankings[ company_number == "00001615" ]
# holders_rankings[ company_number == "SO307326" ]
# holders_rankings[ company_number == "00000529" ]
# Merge the taus
for( a in alphas) {
if( which(alphas == a) == 1 ) {
kendall_taus_participant_ranks <- merge(tau_dpi_npi, get(paste0("tau_dpi_transitive", a)), by = "company_number", all = T)
kendall_taus_participant_ranks <- merge(kendall_taus_participant_ranks, get(paste0("tau_npi_transitive", a)), by = "company_number", all = T)
} else {
kendall_taus_participant_ranks <- merge(kendall_taus_participant_ranks, get(paste0("tau_dpi_transitive", a)), by = "company_number", all = T)
kendall_taus_participant_ranks <- merge(kendall_taus_participant_ranks, get(paste0("tau_npi_transitive", a)), by = "company_number", all = T)
}
message(a)
}
# Add the information on the count of holders
kendall_taus_participant_ranks <- merge(kendall_taus_participant_ranks, unique(holders_rankings[, c("company_number", "countholders_dpi", "countholders_npi", paste0("countholders_transitive", alphas)), with = F], by = "company_number"), by = "company_number", all.x = T, all.y = F)
# Save point
fwrite(kendall_taus_participant_ranks, file = "output/alphaicon_paper/kendall_taus_participant_ranks_dpi_npi_transitive_uk_organisations_participants_2021_7sep21.csv")
############
# Analyse the agreement between rankings
library(data.table)
library(ggplot2)
library(ggthemes)
library(ggrepel)
library(stringi)
library(stringr)
library(stargazer)
library(showtext)
setwd(Sys.getenv('ALPHAICON_PATH'))
# Add the font to use
font_add_google("Open Sans", "Open Sans")
showtext_auto()
# Load the produced CSV with Kendall's tau-b
taus_longs <- fread("output/alphaicon_paper/kendall_taus_participant_ranks_dpi_npi_transitive_uk_organisations_participants_2021_7sep21.csv", encoding = "UTF-8")
# To long form (each line is method and alpha)
taus <- melt(taus_longs, id.vars = "company_number", measure.vars = names(taus_longs)[grepl("kendalltau", names(taus_longs))], variable.name = "pair", value.name = "tau", na.rm = T, variable.factor = T)
countholders <- melt(taus_longs, id.vars = "company_number", measure.vars = names(taus_longs)[grepl("countholders", names(taus_longs))], variable.name = "algorithm", value.name = "countholders", na.rm = T, variable.factor = T)
# Convert pairs to extract useful information
alg_pairs <- data.table(pair = levels(taus$pair))
alg_pairs[, pair_modif := gsub("kendalltau_", "", pair, fixed = T)]
alg_pairs[, c("algorithm1", "algorithm2") := as.data.table(stri_split_fixed(pair_modif, "_", n = 2, simplify = T))]
alg_pairs[, pair_modif := NULL]
alg_pairs[, pair := factor(pair, levels = levels(taus$pair))]
alg_pairs[, alpha := NA_real_ ]
alg_pairs[ grepl("transitive", algorithm2), alpha := as.numeric(gsub("transitive", "", algorithm2))]
alg_pairs[ grepl("transitive", algorithm2), algorithm2 := gsub("[^transitive]", "", algorithm2)]
alg_pairs[, algorithm1 := factor(algorithm1, levels = c("dpi", "npi", "transitive"))]
alg_pairs[, algorithm2 := factor(algorithm2, levels = c("dpi", "npi", "transitive"))]
taus <- merge(taus, alg_pairs, by = "pair")
taus[, pair := NULL]
gc()
# Same for countholders
alg_counts <- data.table(algorithm = levels(countholders$algorithm))
alg_counts[, alg_modif := gsub("countholders_", "", algorithm)]
alg_counts[ grepl("transitive", alg_modif), alpha := as.numeric(gsub("transitive", "", alg_modif))]
alg_counts[ grepl("transitive", alg_modif), alg_modif := gsub("[^transitive]", "", alg_modif)]
alg_counts[, alg_modif := factor(alg_modif, levels = c("dpi", "npi", "transitive"))]
countholders <- merge(countholders, alg_counts, by = "algorithm")
countholders[, algorithm := NULL]
setnames(countholders, "alg_modif", "algorithm")
gc()
# Add count holders to tau
#taus <- merge(taus, countholders, by.x = c("algorithm1", "alpha"), by.y = c("algorithm", "alpha"))
#setnames(taus, "countholders", "countholders1")
#taus <- merge(taus, countholders, by.x = c("algorithm2", "alpha"), by.y = c("algorithm", "alpha"))
#setnames(taus, "countholders", "countholders2")
# Add entity industry to the data (peak use of 40 GB)
taus[, industrysection := uk_basic_companies_data[ match(taus$company_number, uk_basic_companies_data$CompanyNumber)]$industrysection_1 ]
gc()
# Summary statistics of Kendall's tau-b
## Mean, overall
taus_overall_mean <- taus[!is.na(tau), list(tau = mean(tau), tausemean = sd(tau)/sqrt(.N)), by = c("algorithm1", "algorithm2", "alpha")]
## Mean, by industry
taus_industry_mean <- taus[!is.na(tau) & !is.na(industrysection), list( tau = mean(tau), tausemean = sd(tau)/sqrt(.N)), by = c("algorithm1", "algorithm2", "alpha", "industrysection")]
# Export point
#fwrite(taus_overall_mean, file = "output/alphaicon_paper/mean_kendall_taus_participant_ranks_dpi_npi_transitive_uk_organisations_participants_2021_7sep21.csv")
#fwrite(taus_industry_mean, file = "output/alphaicon_paper/mean_by_industrysection_kendall_taus_participant_ranks_dpi_npi_transitive_uk_organisations_participants_2021_7sep21.csv")
# Produce the plot with overall mean
taus_overall_mean[ grepl("dpi|npi", algorithm1), algorithm1 := toupper(algorithm1)]
## Other algorithms vs best and worst-performing transitive algorithm
taus_mean_plot <- ggplot(aes(x = alpha, y = tau, group = algorithm1, color = algorithm1), data = taus_overall_mean[ algorithm1 == "NPI" & algorithm2 == "transitive"]) +
geom_line(size = 1.5, alpha = 1) +
geom_point(size = 2) +
geom_text(aes(label = round(tau, 4)), size = 2.5, nudge_y = 0.0005) +
scale_x_continuous( breaks = c(seq(0, 0.9, 0.1), 0.999), labels = c(seq(0, 0.9, 0.1), 0.999), guide = guide_axis(n.dodge = 1)) +
#facet_wrap(. ~ algorithm1, scales = "free_y")+
labs(y = expression("Kendall's "~tau~"-b betw. NPI\nand "~alpha~"-ICON SH ranks"), x = expression(alpha)) +
scale_colour_brewer(type = "qual", palette = 2) +
theme_minimal() + theme(legend.position = "none", text = element_text(size = 14, family = "Open Sans"), panel.grid.major = element_blank(), panel.grid.minor = element_blank())
#ggsave(taus_mean_plot, file = "output/alphaicon_paper/taus_mean_plot.pdf", width = 8.5, height = 4, device = cairo_pdf, scale = 1)
# Export to a table
#stargazer(taus_overall_mean[ algorithm1 == "NPI" & algorithm2 == "transitive"], type = "latex", summary = F, out = "output/alphaicon_paper/taus_overall_mean.tex", float = F, multicolumn = T, digits = 5)

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# This code reads in the JSONL with daily
# Persons with Significant Control snapshot
# and saves the data on control in long format
# to a cleaned .rdata object
library(data.table)
library(ndjson)
library(lubridate)
library(stringi)
library(stringr)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Stream in the JSONL with daily Persons with Significant Control
# information from http://download.companieshouse.gov.uk/en_pscdata.html
# (takes about 2 hours to load)
psc_snapshot <- ndjson::stream_in("data/uk/persons-with-significant-control-snapshot-2021-08-02.txt", cls = "dt")
# Unify the names
names(psc_snapshot) <- gsub("^data\\.", "", names(psc_snapshot), perl = T)
# Coerce variables to relevant types
## To dates
to_ymd_dates <- unique(c("ceased_on", "notified_on", names(psc_snapshot)[grepl("exempt_from|exempt_to", names(psc_snapshot))]))
psc_snapshot[, c(to_ymd_dates) := lapply(.SD, ymd), .SDcols = to_ymd_dates ]
# Remove last row with overall statistics
psc_snapshot[, c("exemptions_count", "generated_at", "persons_of_significant_control_count", "statements_count") := NULL ]
psc_snapshot <- psc_snapshot[!is.na(company_number)]
# Remove exemptions
psc_snapshot <- psc_snapshot[ kind != "exemptions"]
psc_snapshot[, names(psc_snapshot)[grepl("exempt", names(psc_snapshot))] := NULL ]
# Remove statements
psc_snapshot <- psc_snapshot[ kind != "persons-with-significant-control-statement" ]
psc_snapshot[, statement := NULL ]
# Remove variables with all NAs
na_count <- sapply(psc_snapshot, function(y) sum(length(which(is.na(y)))))
empty_vars <- names(na_count[ which( nrow(psc_snapshot) - na_count == 0) ])
psc_snapshot[, c(empty_vars) := NULL ]
# Kind to factor
psc_snapshot[, kind := as.factor(kind)]
# Save point
save(psc_snapshot, file = "data/uk/psc_snapshot_2021-08-02.rdata", compress = "gzip")

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# This code reads in the CSV with data
# on live UK companies and saves the data
# to a cleaned .rdata object
library(data.table)
library(lubridate)
library(stringi)
library(stringr)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Read in the CSV with Free Company Data Product snapshot
# from http://download.companieshouse.gov.uk/en_output.html
uk_basic_companies_data <- fread("data/uk/BasicCompanyDataAsOneFile-2021-08-01.csv", encoding = "UTF-8", na.strings = "")
# Remove certain columns
cols_to_remove <- names(uk_basic_companies_data)[ grepl("PreviousName|Mortgages|ConfStmt", names(uk_basic_companies_data))]
uk_basic_companies_data[, c(cols_to_remove) := NULL ]
# Empty to NA
for(j in seq_along(uk_basic_companies_data)) {
set(uk_basic_companies_data, i = which(uk_basic_companies_data[[j]] == ""), j=j, value = NA)
}
# Convert dates
cols_to_date <- names(uk_basic_companies_data)[ grepl("Date", names(uk_basic_companies_data))]
uk_basic_companies_data[, c(cols_to_date) := lapply(.SD, dmy), .SDcols = cols_to_date ]
# Vars to factor
cols_to_factor <- c("RegAddress.Country", "CompanyCategory", "CompanyStatus", "CountryOfOrigin", "Accounts.AccountCategory")
uk_basic_companies_data[, c(cols_to_factor) := lapply(.SD, as.factor), .SDcols = cols_to_factor ]
# Split into industry code and industry name
uk_basic_companies_data[, SICCode.SicText_1 := as.character(SICCode.SicText_1) ]
uk_basic_companies_data[, SICCode.SicText_2 := as.character(SICCode.SicText_2) ]
uk_basic_companies_data[, SICCode.SicText_3 := as.character(SICCode.SicText_3) ]
uk_basic_companies_data[, SICCode.SicText_4 := as.character(SICCode.SicText_4) ]
uk_basic_companies_data[, c("industrycode_1", "industryname_1") := as.data.table(stri_split_fixed(SICCode.SicText_1, " - ", n = 2, simplify = T))]
uk_basic_companies_data[, c("industrycode_2", "industryname_2") := as.data.table(stri_split_fixed(SICCode.SicText_2, " - ", n = 2, simplify = T))]
uk_basic_companies_data[, c("industrycode_3", "industryname_3") := as.data.table(stri_split_fixed(SICCode.SicText_3, " - ", n = 2, simplify = T))]
uk_basic_companies_data[, c("industrycode_4", "industryname_4") := as.data.table(stri_split_fixed(SICCode.SicText_4, " - ", n = 2, simplify = T))]
# Fix empty entries
uk_basic_companies_data[ nchar(industryname_1) < 2, industrycode_1 := NA_character_]
uk_basic_companies_data[ nchar(industryname_1) < 2, industryname_1 := NA_character_]
uk_basic_companies_data[ nchar(industryname_2) < 2, industrycode_2 := NA_character_]
uk_basic_companies_data[ nchar(industryname_2) < 2, industryname_2 := NA_character_]
uk_basic_companies_data[ nchar(industryname_3) < 2, industrycode_3 := NA_character_]
uk_basic_companies_data[ nchar(industryname_3) < 2, industryname_3 := NA_character_]
uk_basic_companies_data[ nchar(industryname_4) < 2, industrycode_4 := NA_character_]
uk_basic_companies_data[ nchar(industryname_4) < 2, industryname_4 := NA_character_]
uk_basic_companies_data[, c("SICCode.SicText_1", "SICCode.SicText_2", "SICCode.SicText_3", "SICCode.SicText_4") := NULL ]
# Load SIC 2007 numeric coding of industries
sic_codes <- fread("data/uk/sic_2007_code_list.csv", encoding = "UTF-8", na.strings = "", colClasses = "character")
# Add leading zeros to industry codes
sic_codes[ nchar(sic_code) == 4, sic_code := paste0("0", sic_code) ]
# Debug
#uk_basic_companies_data[ industryname_1 %in% sic_codes[ substr(sic_code, 1, 1) == "0" ]$sic_description & substr(industrycode_1, 1, 1) != "0" ]
#uk_basic_companies_data[ industryname_2 %in% sic_codes[ substr(sic_code, 1, 1) == "0" ]$sic_description & substr(industrycode_2, 1, 1) != "0" ]
# Add industry section
uk_basic_companies_data[, industrysection_1 := sic_codes[ match(substr(uk_basic_companies_data$industrycode_1, 1, 2), substr(sic_codes$sic_code, 1, 2)) ]$section_description ]
uk_basic_companies_data[ industrycode_1 == "99999", industrysection_1 := NA ]
uk_basic_companies_data[, industrysection_2 := sic_codes[ match(substr(uk_basic_companies_data$industrycode_2, 1, 2), substr(sic_codes$sic_code, 1, 2)) ]$section_description ]
uk_basic_companies_data[ industrycode_2 == "99999", industrysection_2 := NA ]
uk_basic_companies_data[, industrysection_3 := sic_codes[ match(substr(uk_basic_companies_data$industrycode_3, 1, 2), substr(sic_codes$sic_code, 1, 2)) ]$section_description ]
uk_basic_companies_data[ industrycode_3 == "99999", industrysection_3 := NA ]
uk_basic_companies_data[, industrysection_4 := sic_codes[ match(substr(uk_basic_companies_data$industrycode_4, 1, 2), substr(sic_codes$sic_code, 1, 2)) ]$section_description ]
uk_basic_companies_data[ industrycode_4 == "99999", industrysection_4 := NA ]
# Factor coercion for industry codes
industry_names <- unique(c(uk_basic_companies_data$industryname_1, uk_basic_companies_data$industryname_2, uk_basic_companies_data$industryname_3, uk_basic_companies_data$industryname_4))
industry_names <- industry_names[!is.na(industry_names)]
industry_names <- industry_names[order(industry_names)]
industry_sections <- unique(c(uk_basic_companies_data$industrysection_1, uk_basic_companies_data$industrysection_2, uk_basic_companies_data$industrysection_3, uk_basic_companies_data$industrysection_4))
industry_sections <- industry_sections[!is.na(industry_sections)]
industry_sections <- industry_sections[order(industry_sections)]
uk_basic_companies_data[, industryname_1 := factor(industryname_1, levels = industry_names) ]
uk_basic_companies_data[, industryname_2 := factor(industryname_2, levels = industry_names) ]
uk_basic_companies_data[, industryname_3 := factor(industryname_3, levels = industry_names) ]
uk_basic_companies_data[, industryname_4 := factor(industryname_4, levels = industry_names) ]
uk_basic_companies_data[, industrysection_1 := factor(industrysection_1, levels = industry_sections) ]
uk_basic_companies_data[, industrysection_2 := factor(industrysection_2, levels = industry_sections) ]
uk_basic_companies_data[, industrysection_3 := factor(industrysection_3, levels = industry_sections) ]
uk_basic_companies_data[, industrysection_4 := factor(industrysection_4, levels = industry_sections) ]
# Save point
save(uk_basic_companies_data, file = "data/uk/uk_basic_companies_data_2021-08-01.rdata", compress = "gzip")

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# This code converts PSC data into
# a long CSV with entity-participant
# mapping that we will in the study
library(data.table)
library(lubridate)
library(stringi)
library(stringr)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Load the PSC snapshot (prepared by 1a_process_psc_snapshot.r)
load("data/uk/psc_snapshot_2021-08-02.rdata")
# Load the companies data as well (prepared by 1b_process_companies_data.r)
load("data/uk/uk_basic_companies_data_2021-08-01.rdata")
# Keep only active companies and exclude data on secret participants
participants <- psc_snapshot[ is.na(ceased) & is.na(ceased_on) & company_number %in% uk_basic_companies_data[ CompanyStatus == "Active"]$CompanyNumber & kind != "super-secure-person-with-significant-control", c("company_number", "date_of_birth.month", "date_of_birth.year", "kind", "name", "name_elements.forename", "name_elements.middle_name", "name_elements.surname", "identification.country_registered", "identification.registration_number", names(psc_snapshot)[grepl("natures_of_control", names(psc_snapshot))] ), with = F ]
# Create participant name
## For individuals it is a concatenation of name and DOB
participants[kind == "individual-person-with-significant-control", participant_name := paste(toupper(name_elements.forename), toupper(name_elements.middle_name), toupper(name_elements.surname), date_of_birth.year, date_of_birth.month, sep = "$") ]
## For entities it is a concatenation of name, ID and country of incorporation
participants[kind != "individual-person-with-significant-control", participant_name := paste(toupper(name), toupper(identification.country_registered), toupper(identification.registration_number), sep = "$") ]
## Add NAs
participants[is.na(name) & is.na(name_elements.forename) & is.na(name_elements.middle_name) & is.na(name_elements.surname), participant_name := NA ]
# Participant ID is either domestic company number or individual name
## Consider company number as identifier
participants[ grepl("England|scotland|wales|^uk$|uk\\s+|United Kingdom|Great Britain|london|Cardiff|Engalnd|E\\&W|britain|Gb-Sct|N\\.Ireland|N\\. Ireland|Englan|Englad|Engand|Companies House|United Kindom|U\\.K|Gb-Nir|Unitied Kingdom|United Kingom|Endland|Great Britian|United Kigdom|Northern Ireland|Belfast|Englang|Gb-Wls|Kent|Enland|Sotland|Rngland|Englane|Scotlan|Englanf|Enagland|Staffordshire|Northen Ireland|Enagland|Englang|Englamd|Northamptonshire|Engkand|Emgland|England|United Kingtom|English|Devon|Durham|Stirlingshire|Register Of Companies|United Kingdo|Unitedd Kingdom|United Kingd|Scotlnd|Cumbria|Renfrewshire|Uunited Kingdom|Noerthern Ireland|Shropshire|Englabnd|Uk Company|United Kingdown|United King|U\\. K\\.|Ukl", identification.country_registered, perl = T, ignore.case = T) & identification.registration_number %in% unique(c(uk_basic_companies_data$CompanyNumber, psc_snapshot$company_number)), participant_id := identification.registration_number ]
## Create unique company name-company number mapping
## to restore company numbers
uk_company_name_number_mapping <- uk_basic_companies_data[, list(count_samename = .N), by = c("CompanyName") ]
uk_company_name_number_mapping <- uk_company_name_number_mapping[ count_samename == 1 ]
uk_company_name_number_mapping[, company_number := uk_basic_companies_data[ match(uk_company_name_number_mapping$CompanyName, uk_basic_companies_data$CompanyName)]$CompanyNumber ]
uk_company_name_number_mapping[, count_samename := NULL ]
## Add this to participant IDs
participants[ kind == "corporate-entity-person-with-significant-control", participant_id_namebased := uk_company_name_number_mapping[ match(toupper(participants[kind == "corporate-entity-person-with-significant-control"]$name), toupper(uk_company_name_number_mapping$CompanyName))]$company_number]
## Perform the replacement (about 95 thousand companies more now have proper IDs)
participants[ kind == "corporate-entity-person-with-significant-control" & is.na(participant_id) & !is.na(participant_id_namebased), participant_id := participant_id_namebased ]
participants[, participant_id_namebased := NULL ]
## If match on company ID fails, use the name-dob combination
participants[is.na(participant_id), participant_id := participant_name ]
# Remove irrelevant fields (except for "kind" as it is crucial in determining the participant_id)
participants[, c("date_of_birth.month", "date_of_birth.year", "name", "name_elements.forename", "name_elements.middle_name", "name_elements.surname", "identification.country_registered", "identification.registration_number", "participant_name") := NULL ]
# Remove possible duplicates
nrow(participants) # 5502058
participants <- unique(participants, by = c("company_number", "participant_id"))
nrow(participants) # 5482200
# To long data to obtain equity shares
participants_long <- melt(participants, id.vars = c("company_number", "participant_id"), value.name = "nature_of_control", na.rm = T)
participants_long[, variable := NULL ]
participants_long[, equity_share := NA_real_]
participants_long[grepl("25-to-50", nature_of_control, perl = T), equity_share := 37.5]
participants_long[grepl("50-to-75", nature_of_control, perl = T), equity_share := 62.5]
participants_long[grepl("75-to-100", nature_of_control, perl = T), equity_share := 87.5]
# Back to participants data, but now with equity share
temp <- participants_long[, list(equity_share = max(equity_share, na.rm = T)), by = c("company_number", "participant_id")]
temp[!is.finite(equity_share), equity_share := NA]
participants <- merge(participants[, c("company_number", "participant_id", "kind"), with = F], temp, by = c("company_number", "participant_id"), all = F, sort = F)
# Replace NAs with proper value of full ownership if we have one person per entity
participants[, persons_per_entity := .N, by = "company_number" ]
participants[persons_per_entity == 1 & is.na(equity_share), equity_share := 87.5 ]
participants[, persons_per_entity := NULL ]
# Shorter kinds
participants[ kind == "individual-person-with-significant-control", kind := "individual" ]
participants[ kind == "corporate-entity-person-with-significant-control", kind := "entity" ]
participants[ kind == "legal-person-person-with-significant-control", kind := "legal_person" ]
# Proper order and save point
setorderv(participants, c("company_number", "participant_id"))
# Save point
fwrite(participants, file = "output/uk/uk_organisations_participants_2021_long_2aug21.csv", eol = "\n")

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# This code processes the dump of
# CorpWatch EDGAR data to create
# a CSV with entity-participant
# mapping from SEC 10-K Exhibit 21
# that we will use in the study
library(data.table)
library(lubridate)
library(stringi)
library(stringr)
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Load the data from http://api.corpwatch.org/ dump
# (http://api.corpwatch.org/documentation/db_dump/)
## Company information (name, id, location)
## This information includes data on parent-subsidiary relationship
company_info <- fread("data/corpwatch_api_tables_csv_14aug21/company_info.csv", encoding = "UTF-8", na.strings = c("", "NULL"))
## Company locations
company_locations <- fread("data/corpwatch_api_tables_csv_14aug21/company_locations.csv", encoding = "UTF-8", na.strings = c("", "NULL"))
## Company name-id mapping
cik_name_lookup <- fread("data/corpwatch_api_tables_csv_14aug21/cik_name_lookup.csv", encoding = "UTF-8", na.strings = c("", "NULL"))
## Add locations to the company information
company_info[, country := company_locations[ match(company_info$best_location_id, company_locations$location_id) ]$country_code ]
### Extract subsidiaries of UK companies active in 2020--2021 (whichever comes latest)
uk_subsidiary_companies_filers <- company_info[ year >= 2020 & country == "GB" & top_parent_id != cw_id, c("year", "company_name", "cw_id", "num_parents", "num_children", "top_parent_id"), with = F]
### Get the latest available year
setorderv(uk_subsidiary_companies_filers, c("cw_id", "year"), c(1, -1))
uk_subsidiary_companies_filers <- unique(uk_subsidiary_companies_filers, by = c("cw_id"))
uk_subsidiary_companies_filers[, year := NULL ]
## Parent-subsidiary ID mapping
uk_parent_subsidiary_mapping <- unique(uk_subsidiary_companies_filers[, c("cw_id", "top_parent_id", "company_name")])
setnames(uk_parent_subsidiary_mapping, c("subsidiary_cw_id", "parent_cw_id", "subsidiary_name"))
# Add namesakes
## For subsidiaries
uk_parent_subsidiary_mapping <- merge(uk_parent_subsidiary_mapping, cik_name_lookup[, c("cw_id", "edgar_name")], by.x = "subsidiary_cw_id", by.y = "cw_id", all.x = T, all.y = F)
uk_parent_subsidiary_mapping[!is.na(edgar_name) & subsidiary_name != edgar_name, subsidiary_name := edgar_name ]
uk_parent_subsidiary_mapping[, edgar_name := NULL ]
## For parents
uk_parent_subsidiary_mapping[, parent_name := company_info[year >= 2020][ match(uk_parent_subsidiary_mapping$parent_cw_id, company_info[year >= 2020]$cw_id) ]$company_name ]
uk_parent_subsidiary_mapping <- merge(uk_parent_subsidiary_mapping, cik_name_lookup[, c("cw_id", "edgar_name")], by.x = "parent_cw_id", by.y = "cw_id", all.x = T, all.y = F)
uk_parent_subsidiary_mapping[ !is.na(edgar_name) & parent_name != edgar_name, parent_name := edgar_name ]
uk_parent_subsidiary_mapping[, edgar_name := NULL ]
uk_parent_subsidiary_mapping <- unique(uk_parent_subsidiary_mapping)
# Remove self-loops
uk_parent_subsidiary_mapping <- uk_parent_subsidiary_mapping[ subsidiary_cw_id != parent_cw_id ]
uniqueN(uk_parent_subsidiary_mapping$parent_cw_id) # 1071
uniqueN(uk_parent_subsidiary_mapping$subsidiary_cw_id) # 7634
# Match the parent-subsidiart data from SEC filings with PSC register on company names
## Load the companies data prepared by 1b_process_companies_data.r
load("data/uk/uk_basic_companies_data_2021-08-01.rdata")
## Load the participants panel prepared by 2_psc_snapshot_to_participants_panel.r
participants <- fread("output/uk/uk_organisations_participants_2021_long_2aug21.csv", encoding = "UTF-8", na.strings = "")
## Keep only entities-persons with significant control
participants <- participants[ kind %in% c("entity", "legal_person") ]
## Add the names to the participants panel
participants[, company_name := uk_basic_companies_data[ match(participants$company_number, uk_basic_companies_data$CompanyNumber) ]$CompanyName ]
participants[, participant_name := uk_basic_companies_data[ match(participants$participant_id, uk_basic_companies_data$CompanyNumber) ]$CompanyName ]
participants[, participant_name_bak := stri_split_fixed(participant_id, "$", n = 2, simplify = T)[,1] ]
participants[ is.na(participant_name) & !is.na(participant_name_bak), participant_name := participant_name_bak ]
participants[, participant_name_bak := NULL ]
## Reduce the names of companies
### Name cleaner function
name_cleaner <- function(x) {
out <- gsub("(['’\n ]|[[:punct:]]|[[:space:]]|[[:cntrl:]])+", " ", x, perl = T)
out <- gsub(" LIMITED", " LTD", out, perl = T, ignore.case = T)
out <- str_trim(out)
return(out)
}
### Remove punctuation, stopwords, strip whitespaces from company_names
participants[, company_name_reduced := name_cleaner(toupper(company_name))]
participants[, participant_name_reduced := name_cleaner(toupper(participant_name))]
uk_parent_subsidiary_mapping[, subsidiary_name_reduced := name_cleaner(toupper(subsidiary_name)) ]
uk_parent_subsidiary_mapping[, parent_name_reduced := name_cleaner(toupper(parent_name)) ]
# UK company number - name mapping excluding namesakes
uk_company_name_number_mapping <- unique(participants[, c("company_number", "company_name_reduced"), with = F])
uk_company_name_number_mapping[, count_namesakes := .N, by = "company_name_reduced" ]
uk_company_name_number_mapping <- uk_company_name_number_mapping[ count_namesakes == 1]
uk_company_name_number_mapping[, count_namesakes := NULL ]
# Participant id - participant name mapping excluding namesakes
uk_participant_name_id_mapping <- unique(participants[, c("participant_id", "participant_name_reduced"), with = F])
uk_participant_name_id_mapping[, count_namesakes := .N, by = "participant_name_reduced" ]
uk_participant_name_id_mapping <- uk_participant_name_id_mapping[ count_namesakes == 1]
uk_participant_name_id_mapping[, count_namesakes := NULL ]
# Add company numbers to UK subsidiary companies from SEC 10-K Exhibit 21
uk_parent_subsidiary_mapping[, company_number := uk_company_name_number_mapping[ match(uk_parent_subsidiary_mapping$subsidiary_name_reduced, uk_company_name_number_mapping$company_name_reduced) ]$company_number ]
# Add participant_ids to parent companies from SEC 10-K Exhibit 21
uk_parent_subsidiary_mapping[, participant_id := uk_participant_name_id_mapping[ match(uk_parent_subsidiary_mapping$parent_name_reduced, uk_participant_name_id_mapping$participant_name_reduced) ]$participant_id ]
# Final list with only matched entries, excluding
# namesakes
uk_parent_subsidiary_mapping <- unique(uk_parent_subsidiary_mapping[ !is.na(company_number) & !is.na(participant_id), c("company_number", "participant_id", "subsidiary_cw_id", "parent_cw_id") ], by = c("company_number", "participant_id"))
# Export point
fwrite(uk_parent_subsidiary_mapping, file = "data/uk/uk_parent_subsidiary_mapping_2020_2021_sec_filers_exhibit21.csv", eol = "\n")

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# This code implements Algorithm 1
# "Label propagation for NPI"
# from Mizuno, Doi, and Kurizaki (2020, p. 7)
# (https://doi.org/10.1371/journal.pone.0237862)
library(data.table)
# Function to compute Network or Direct power index
# INPUTS: a data.table with participant-entity relations
# in long form or an igraph object with edge weights
# OUTPUTS: data.table with power index for each participant
# or named list with such table and labels from each iteration
# (if save_labels = T).
compute_power_index <- function(relations_object,
participant_var = "participant",
entity_var = "entity",
weight_var = "weight",
powerindex = "dpi", # which power index to compute
iterations = 100, # how many iterations to run
quota = 50, # majority rule, %
epsilon = 0.01, # probability to restore the original label when computing the NPI
iterations_to_discard = 20, # how many iterations to discard when computing the NPI
save_labels = FALSE # whether to save labels from each iteration
) {
# Debug: powerindex <- "dpi"; iterations <- 100; quota <- 50; epsilon <- 0.01; iterations_to_discard <- 20; save_labels <- F; participant_var = "participant"; entity_var = "entity"; weight_var = "voting_share"
# Input checks
## Does the relations object exist and is it in correct form?
stopifnot("relations_object is not specified" = !missing(relations_object))
## If the relations object is in igraph transform to a data.frame
if( "igraph" %in% class(relations_object) ) {
relations_object <- igraph::as_data_frame(relations_object, what = "edges")
# Check whether a weight column is present in the data (i.e. data.frame has at least 3 columns
stopifnot("`relations_object` graph does not have edge weights" = ncol(relations_object) >= 3)
# Proper names
names(relations_object)[1:2] <- c(participant_var, entity_var)
}
## If the relations object is not a data.table try to coerce to it
if( !("data.table" %in% class(relations_object)) ) {
data.table::setDT(relations_object)
}
## Are the participant and entity variables in the data?
stopifnot("`participant_var` variable not found in `relations_object`" = participant_var %in% names(relations_object))
stopifnot("`entity_var` variable not found in `relations_object`" = entity_var %in% names(relations_object))
stopifnot("`weight_var` variable not found in `relations_object`" = weight_var %in% names(relations_object))
## Are the power index options correctly specified?
stopifnot("`powerindex` should be either dpi or npi" = powerindex %in% c("npi", "dpi"))
stopifnot("`save_labels` should be either TRUE or FALSE" = save_labels %in% c(TRUE, FALSE))
## Are the parameters of the required type?
stopifnot("`iterations should` be an integer" = all.equal(iterations, as.integer(iterations)) )
stopifnot("`iterations_to_discard` should be an integer not exceeding `iterations`" = (all.equal(iterations_to_discard, as.integer(iterations_to_discard)) & iterations_to_discard < iterations) | powerindex == "dpi" )
min_weight <- min(relations_object[[weight_var]], na.rm = T)
max_weight <- max(relations_object[[weight_var]], na.rm = T)
stopifnot("`weight_var` should take non-negative numeric values" = min_weight >= 0 & is.finite(max_weight) & is.finite(min_weight) )
stopifnot("epsilon should be in [0,1] range" = (epsilon >= 0 & epsilon <= 1) | powerindex == "dpi" )
## Disable the `iterations_to_discard` option
## when computing DPI
if( powerindex == "dpi" ) {
iterations_to_discard <- 0
}
# Remove observations with missing data
## Participant
if( nrow(relations_object[ is.na(get(participant_var)) ]) > 0 ) {
warning(paste0("Removing rows with missing ", participant_var, " before computation"))
relations_object <- relations_object[ !is.na(get(participant_var)) ]
}
## Entity
if( nrow(relations_object[ is.na(get(entity_var)) ]) > 0 ) {
warning(paste0("Removing rows with missing ", entity_var, " before computation"))
relations_object <- relations_object[ !is.na(get(entity_var)) ]
}
## Weight
if( nrow(relations_object[ is.na(get(weight_var)) ]) > 0 ) {
warning(paste0("Removing rows with missing ", weight_var, " before computation"))
relations_object <- relations_object[ !is.na(get(weight_var)) ]
}
# Init an object to update labels in each iteration
updating_relations <- copy(relations_object[, c(participant_var, entity_var, weight_var), with = F])
setnames(updating_relations, c("participant", "entity", "weight"))
# Init an object to store per-iteration
# entity labels (i.e. who the pivotal
# shareholder is)
if( save_labels == T) {
iteration_labels <- data.table()
# Otherwise we store overall counts of each
# label being named a pivot
} else {
pivot_counts <- updating_relations[, c("participant", "entity")]
pivot_counts[, times_pivotal := 0 ]
}
# Create a progress bar to report on iteration progess
message(paste0("Iterating through ", iterations, " permutations:"))
iterations_progess_bar <- txtProgressBar(min = 0, max = iterations, style = 3)
for(i in 1:iterations) {
# Randomly order rows within entities
updating_relations[, random_var := runif(.N)]
setorderv(updating_relations, c("entity", "random_var"))
# Breaking cycles when computing NPI: restore original
# labels for the random set of rows with epsilon
# probability
if( powerindex == "npi" & epsilon > 0 ) {
entities_to_restore <- unique(updating_relations[ random_var <= epsilon ]$entity)
if( length(entities_to_restore) > 0 ) {
restored_entities <- relations_object[ get(entity_var) %in% entities_to_restore, c(participant_var, entity_var, weight_var), with = F]
setnames(restored_entities, c("participant", "entity", "weight"))
# Randomly shuffle the labels to restore as well respect random ordering
restored_entities[, random_var := runif(.N) ]
setorderv(restored_entities, c("entity", "random_var"))
updating_relations <- rbind(updating_relations[ !( entity %in% entities_to_restore) ],
restored_entities,
fill = T)
}
}
# Compute cumulative sums of voting rights by entity
updating_relations[, cumulative_weight := cumsum(weight), by = "entity"]
# Lagged cumulative voting share
# shift() is not optimized with many groups
# (https://github.com/Rdatatable/data.table/issues/1534)
# so we cannot simply use `by` statement as below
# updating_relations[, cumulative_weight_l1 := shift(cumulative_weight, type = "lag", n = 1), by = "entity"]
#
# Instead, consider a two-step hack that uses our entity ordering
# to mark as missing lagged weights for the first participant per entity
updating_relations[, cumulative_weight_l1 := shift(cumulative_weight, type = "lag", n = 1)]
updating_relations[, entity_l1 := shift(entity, type = "lag", n = 1)]
updating_relations[entity != entity_l1, cumulative_weight_l1 := NA_real_ ]
# Identify pivots
pivots <- updating_relations[ cumulative_weight >= quota & (cumulative_weight_l1 < quota | is.na(cumulative_weight_l1) ), c("participant", "entity") ]
# Store pivots from each iteration in a designated object
if( save_labels == T) {
iteration_labels <- rbind(iteration_labels, data.table(iteration = i, pivots), fill = T)
# NB: ^ this is the most problematic step in terms of scaling.
# Where to store and access an N * number of iterations table
# with labels when N is huge and iterations = 20 000? We need
# to save pivots for ~3 million entities 20 thousand times.
#
# Alternatively you can write pivots from each iteration to a separate CSV
# but you will still end up with 20 thousand files, each having ~3 million lines.
}
# We can avoid storing the pivots altogether and just
# add to the total count of times a given partipant is
# named pivotal in a given entity. We also discard
# the first `iterations_to_discard` iterations
if( save_labels == F & i > iterations_to_discard ) {
# We row bind the current pivots to the existing counts
# and then sum. This might be faster than merging on
# entity and participant.
# In fact, it is very slow
pivot_counts <- rbind(pivot_counts, data.table(pivots, times_pivotal = 1), fill = T)
pivot_counts <- pivot_counts[, list( times_pivotal = sum(times_pivotal) ), by = c("entity", "participant")]
}
# When computing NPI: update the participant
# labels with pivots identified during this
# iteration step
if( powerindex == "npi" ) {
updating_relations[, participant_update := pivots[ match(updating_relations$participant, pivots$entity) ]$participant ]
updating_relations[ !is.na(participant_update), participant := participant_update ]
updating_relations[, participant_update := NA ]
# Sum up the updated shares for the next iteration
updating_relations <- updating_relations[, list(weight = sum(weight)), by = c("entity", "participant")]
}
# Update the progress bar
setTxtProgressBar(iterations_progess_bar, i)
}
# Compute the index itself
if( save_labels == T ) {
# Count the number of times this
# participant was named the pivotal player,
# discarding first `iterations_to_discard` iterations
index_values <- iteration_labels[iteration > iterations_to_discard, list(times_pivotal = .N), by = c("entity", "participant")]
} else {
index_values <- pivot_counts
}
# Compute the index
index_values[, index := times_pivotal/(iterations - iterations_to_discard) ]
setnames(index_values, "index", powerindex)
if( save_labels == T ) {
return(list(index_values = index_values, iteration_labels = iteration_labels))
} else {
return(index_values)
}
}

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# Install the required dependencies
# Declare working directory beforehand in an environment variable
# ALPHAICON_PATH = "path_to_your_folder"
# with the aid of usethis::edit_r_environ()
# Restart R session for the changes to make effect
setwd(Sys.getenv('ALPHAICON_PATH'))
# Read in the file with dependencies
packages <- readLines(con <- file("DEPENDENCIES", encoding = "UTF-8"))
packages <- gsub("^\\s+", "", packages[2:length(packages)])
packages <- gsub("\\s+.*$", "", packages)
# Install the uninstalled packages
missing_packages <- setdiff(packages, rownames(installed.packages()))
if ( length(missing_packages) > 0 ) {
# Install the latest versions of all the packages
install.packages(missing_packages, quiet = T)
}

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participant_id,participant_name,ranktransitive,ranknpi,rankdpi,sumtransitive,sumnpi,sumdpi,nodes,SH,ST,I,C
SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624,SPECSAVERS OPTICAL SUPERSTORES LTD,1,1,42441,1482.2,1453,4,1767,188,1159,420,0
PETER$NA$VALAITIS$1950$11,PETER VALAITIS,2,2,1,1392,1392,1391,1393,1,1390,2,0
PARTNERS GROUP HOLDING AG$SWITZERLAND$CHE-108.562.489,PARTNERS GROUP HOLDING AG,3,3,2,1166.5,1166.5,1164.5,1170,2,1167,1,0
AVTAR$NA$SINGH$1967$8,AVTAR SINGH,4,4,4,1051,1051,1051,1055,3,1052,0,0
ANDREW$SIMON$DAVIS$1963$7,ANDREW DAVIS,5,6,2788,881.3,869.5,14.5,1020,107,895,18,0
ROBERT$ANTHONY$JARRETT$1974$8,ROBERT JARRETT,6,5,5,873,873,873,874,1,873,0,0
SC095000,LLOYDS BANKING GROUP PLC,7,8,24872,735.6,670.5,5,956,35,596,325,0
CHRIS$NA$HADJIOANNOU$1981$1,CHRIS HADJIOANNOU,8,7,6,730,730,730,731,1,730,0,0
11443992,BRIDGEPOINT GROUP PLC,9,10,5149,669.3,591.5,11,808,13,536,259,0
READE$NA$GRIFFITH$1965$4,READE GRIFFITH,10,9,491331,657.5,636.5,1.5,868,25,374,469,0
PERSIMMON PLC$ENGLAND$1818486,PERSIMMON PLC,11,11,2911,586,578.4,14,617,4,561,52,0
INTERTRUST N.V.$THE NETHERLANDS$N/A,INTERTRUST N.V.,12,12,887094,519.7,511.8,1,530,4,353,173,0
IWG PLC$JERSEY$122154,IWG PLC,13,13,10,481.8,481.7,422,497,6,473,18,0
00604574,BARRATT DEVELOPMENTS P L C,14,17,587,481.1,473.6,31,530,9,446,75,0
06035106,FRASERS GROUP PLC,15,16,2982,480.1,474.8,14,484,2,438,44,0
GRZEGORZ$NA$SZEWCZYK$1985$7,GRZEGORZ SZEWCZYK,16,14,8,480,480,480,481,1,480,0,0
DARREN$NA$SYMES$1958$10,DARREN SYMES,17,15,9,475.5,475.5,474.5,478,2,475,1,0
08885072,PETS AT HOME GROUP PLC,18,19,1226949,468,389.1,1,770,216,514,40,0
10657226,BGF GROUP PLC,19,23,6219,462.1,343,10,674,99,378,197,0
03981143,OCTOPUS CAPITAL LIMITED,20,18,1624,414.5,411.7,19,431,4,310,117,0
11444019,M&G PLC,21,20,17408,404,386.6,6,469,14,298,157,0
00102498,BP P.L.C.,22,26,1757,377.8,336.4,18,493,5,390,96,2
10510800,IVC ACQUISITION PIKCO LTD,23,21,1535931,370,366.3,1,371,1,341,29,0
SUN LIFE FINANCIAL INC.$CANADA$F380,SUN LIFE FINANCIAL INC.,24,22,2086664,364.7,358.2,1,469,10,242,217,0
03777037,PLACES FOR PEOPLE GROUP LIMITED,25,25,458,345.8,338.7,35.5,387,11,324,52,0
KANE$STEVEN JAMES$WALLACE$1988$4,KANE WALLACE,26,24,12,342,342,342,343,1,342,0,0
01417162,LEGAL & GENERAL GROUP PLC,27,28,3477,333.1,321,13,399,14,286,99,0
04569346,DIGNITY PLC,28,27,45566,332.9,328.5,4,348,13,284,51,0
02468686,AVIVA PLC,29,29,58547,316.1,305.8,4,372,11,261,100,0
00621920,BRITISH LAND COMPANY PUBLIC LIMITED COMPANY(THE),30,30,11060,301.8,295.8,7.5,315,1,218,96,0
01142830,3I GROUP PLC,31,35,1948,290.6,276.4,17.3,392,12,176,204,0
00296805,TAYLOR WIMPEY PLC,32,33,6642,289.9,283.3,9.5,339,11,260,68,0
00082548,REACH PLC,33,31,365,289.4,286.7,39,297,1,229,67,0
BRYAN$ANTHONY$THORNTON$1955$7,BRYAN THORNTON,34,32,135,287.3,284.3,70,299,6,290,3,0
08286875,WPP JUBILEE LIMITED,35,36,268,284.8,271.2,45.8,314,6,200,108,0
RONALD$TERENCE$RICHARDS$1945$1,RONALD RICHARDS,36,34,17,280,280,280,281,1,280,0,0
02877315,REDROW PLC,37,37,176901,273.2,269.7,2,292,5,268,19,0
WOODLEY$LARKIN$HUNT$1945$11,WOODLEY HUNT,38,39,1331918,261.3,256.5,1,287,2,154,131,0
HANNOVER RUCK SE$GERMANY$HRB 6778,HANNOVER RUCK SE,39,38,82217,261,258.4,3,262,1,254,7,0
01470151,BAE SYSTEMS PLC,40,42,387,252.9,251.4,38,301,7,206,88,0
ANDREW$ROY$LEIGHTON$1949$10,ANDREW LEIGHTON,41,41,38,252.3,251.4,159.3,256,3,251,2,0
08340090,COUNTRYWIDE LIMITED,42,43,785896,248,245.5,1,249,1,217,31,0
04967001,ITV PLC,43,46,71002,247.9,242.3,3.2,274,16,209,49,0
10763268,CSC FINANCIAL SERVICES HOLDINGS LIMITED,44,44,306820,247.7,245,2,250,1,161,88,0
HEIDELBERGCEMENT AG$GERMANY$HRB 33082,HEIDELBERGCEMENT AG,45,48,210440,246.4,236.1,2,260,3,166,91,0
STEPHEN$ALLEN$SCHWARZMAN$1947$2,STEPHEN SCHWARZMAN,46,45,96,244.7,243.4,90,256,3,171,82,0
OC301825,HGCAPITAL LLP,47,47,2009,242.2,239.1,17,247,4,164,79,0
OC360196,EQUISTONE LLP,48,40,242598,241.6,252.4,2,261,4,167,90,0
03140521,MATTIOLI WOODS PLC,49,55,453,241.1,226.6,35.5,290,22,181,87,0
STEPHEN$STUART SOLOMON$CONWAY$1948$2,STEPHEN CONWAY,50,49,5851,237.5,233.6,10,317,14,230,73,0
CRH PLC$IRELAND$12965,CRH PLC,51,50,617583,235.4,230.1,1,268,7,201,60,0
OC332179,DRUCES LLP,52,52,183094,230.3,227.7,2,234,3,229,2,0
BELLWAY P.L.C.$ENGLAND$1372603,BELLWAY P.L.C.,53,53,1279,229.5,227.3,21,253,4,236,13,0
SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA,SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED,54,51,961566,229.2,229.5,1,270,4,151,115,0
MICHAEL$JOHN$HALL$1971$7,MICHAEL HALL,55,54,22,225.3,226.9,226.8,239,5,234,0,0
00521970,MORGAN SINDALL GROUP PLC,56,61,969,217.9,209.6,24,298,16,205,77,0
BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4,BENZION FRESHWATER,57,56,1526,215.6,216.4,19.5,257,6,222,29,0
MICHAEL$BARRY$TABOR$1941$10,MICHAEL TABOR,58,60,194884,214.8,211.1,2,226,4,161,61,0
00306718,VISTRY GROUP PLC,59,59,173704,213.8,211.2,2,260,7,223,30,0
SC045551,NATWEST GROUP PLC,60,58,42589,213.6,211.5,4,261,8,173,79,1
06397765,OCTOPUS TITAN VCT PLC,61,62,11088,211.1,208.7,7.5,221,4,124,93,0
RADOVAN$NA$KOLJEVIC$1967$5,RADOVAN KOLJEVIC,62,63,47760,211,208.4,4,216,4,204,8,0
05172586,THE BERKELEY GROUP HOLDINGS PLC,63,64,619407,209.2,207.2,1,216,1,202,13,0
SENTTHURAN$NA$NADARAJAH$1979$11,SENTTHURAN NADARAJAH,64,66,3685,207,205.1,13,208,1,206,1,0
JOAQUIM$NA$MAGRO DE ALMEIDA$1949$1,JOAQUIM MAGRO DE ALMEIDA,65,65,27,205.8,205.5,205.5,216,4,212,0,0
OLUWOLE$NA$KOLADE$1966$11,OLUWOLE KOLADE,66,70,57071,204.4,197.2,4,235,10,97,128,0
DAVID$JAMES$BARRICK$1984$1,DAVID BARRICK,67,57,25,201,213.5,213.6,254,1,251,2,0
STACEY$LOUISE$TRAMASEUR$1997$1,STACEY TRAMASEUR,68,67,29,201,201,201,202,1,201,0,0
ROMY$ELIZABETH$SUMMERSKILL$1967$1,ROMY SUMMERSKILL,69,68,15243,200.9,199.1,6.5,217,2,142,73,0
JAY$NA$THOMAS$1981$1,JAY THOMAS,70,69,30,199,199,199,200,1,199,0,0
SC286832,ABRDN PLC,71,74,1623,194,189.6,19,204,5,157,42,0
04120344,WHITBREAD PLC,72,71,592751,193.5,191,1,200,3,170,27,0
KEITH$NA$BRESLAUER$1966$3,KEITH BRESLAUER,73,72,71852,192.9,190.1,3,200,2,131,67,0
OC313101,AUGUST EQUITY LLP,74,73,5699,191.8,189.7,10,194,2,97,92,3
PATRICK$ANTHONY$MCKENNA$1956$6,PATRICK MCKENNA,75,79,13432,185,182.9,7,197,4,167,26,0
GUY$NA$HANDS$1959$8,GUY HANDS,76,77,3793,183.4,183.9,12.5,203,3,157,43,0
REBECCA$LOUISE$CODY$1997$7,REBECCA CODY,77,80,33,182,182,182,183,1,182,0,0
JEAN-GUY$NA$DESJARDINS$1944$10,JEAN-GUY DESJARDINS,78,88,9585,180.7,165.9,8,298,12,208,78,0
00445790,TESCO PLC,79,82,1527,180.4,178.2,19.5,199,4,132,63,0
STEPHEN$JAMES$ROBERTSON$1960$3,STEPHEN ROBERTSON,80,76,156655,178.2,186.6,2.3,383,14,269,100,0
MANJIT$NA$DALE$1965$6,MANJIT DALE,81,92,162072,178.2,163.9,2.3,383,14,269,100,0
THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064,THE BERKELEY GROUP PLC,82,81,381,177.4,178.2,38.5,208,2,165,41,0
MOHAMMED$NA$AYYAZ$1996$12,MOHAMMED AYYAZ,83,83,35,177.3,177.3,177.3,222,30,192,0,0
CERI$NA$JOHN$1955$7,CERI JOHN,84,84,36,176,176,176,177,1,176,0,0
04330127,WILMINGTON TRUST (UK) LIMITED,85,85,185351,174.7,172.4,2,180,2,123,55,0
08379990,LIBERTY GLOBAL PLC,86,96,4578,172.6,162.3,11.5,335,11,239,85,0
VISTRY (JERSEY) LIMITED$JERSEY$130175,VISTRY (JERSEY) LIMITED,87,99,672013,171.8,161.5,1,243,10,186,47,0
07934492,CURTIS BANKS GROUP PLC,88,87,9563,170.8,168.2,8,181,4,161,16,0
00617987,HSBC HOLDINGS PLC,89,102,2511,170.8,160.2,15.2,220,6,150,64,0
BROOKFIELD ASSET MANAGEMENT INC$CANADA$/,BROOKFIELD ASSET MANAGEMENT INC,90,75,555776,170.5,186.6,1,347,4,225,118,0
QATAR INVESTMENT AUTHORITY$QATAR$/,QATAR INVESTMENT AUTHORITY,91,114,2818663,170.5,150.9,1,347,4,225,118,0
06394563,ENDEMOL SHINE GROUP HOLDING UK LIMITED,92,86,78751,170,168.3,3,175,3,142,30,0
OC333409,TRICOR SERVICES EUROPE LLP,93,91,42092,169.8,164.1,4,221,21,159,41,0
SOFTBANK GROUP CORP$JAPAN$0104-01-056795,SOFTBANK GROUP CORP,94,93,80640,168.7,163.8,3,181,5,101,75,0
07023200,ADP PRIMARY CARE SERVICES LIMITED,95,89,962994,167.7,165.8,1,170,1,134,35,0
03199160,THE UNITE GROUP PLC,96,94,42466,164.3,162.7,4,168,2,134,32,0
11499533,SCOOBY BIDCO LIMITED,97,97,1443396,163.9,162.2,1,172,3,143,26,0
00349201,ST. MODWEN PROPERTIES PLC,98,90,195,162.4,164.7,56,200,6,164,30,0
11606773,PHOENIX GROUP HOLDINGS PLC,99,98,93217,161.8,162.1,3,177,3,134,40,0
ANDRZEJ$NA$NIEMYJSKI$1975$11,ANDRZEJ NIEMYJSKI,100,100,37,161.5,161.5,161.5,164,2,162,0,0
1 participant_id participant_name ranktransitive ranknpi rankdpi sumtransitive sumnpi sumdpi nodes SH ST I C
2 SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624 SPECSAVERS OPTICAL SUPERSTORES LTD 1 1 42441 1482.2 1453 4 1767 188 1159 420 0
3 PETER$NA$VALAITIS$1950$11 PETER VALAITIS 2 2 1 1392 1392 1391 1393 1 1390 2 0
4 PARTNERS GROUP HOLDING AG$SWITZERLAND$CHE-108.562.489 PARTNERS GROUP HOLDING AG 3 3 2 1166.5 1166.5 1164.5 1170 2 1167 1 0
5 AVTAR$NA$SINGH$1967$8 AVTAR SINGH 4 4 4 1051 1051 1051 1055 3 1052 0 0
6 ANDREW$SIMON$DAVIS$1963$7 ANDREW DAVIS 5 6 2788 881.3 869.5 14.5 1020 107 895 18 0
7 ROBERT$ANTHONY$JARRETT$1974$8 ROBERT JARRETT 6 5 5 873 873 873 874 1 873 0 0
8 SC095000 LLOYDS BANKING GROUP PLC 7 8 24872 735.6 670.5 5 956 35 596 325 0
9 CHRIS$NA$HADJIOANNOU$1981$1 CHRIS HADJIOANNOU 8 7 6 730 730 730 731 1 730 0 0
10 11443992 BRIDGEPOINT GROUP PLC 9 10 5149 669.3 591.5 11 808 13 536 259 0
11 READE$NA$GRIFFITH$1965$4 READE GRIFFITH 10 9 491331 657.5 636.5 1.5 868 25 374 469 0
12 PERSIMMON PLC$ENGLAND$1818486 PERSIMMON PLC 11 11 2911 586 578.4 14 617 4 561 52 0
13 INTERTRUST N.V.$THE NETHERLANDS$N/A INTERTRUST N.V. 12 12 887094 519.7 511.8 1 530 4 353 173 0
14 IWG PLC$JERSEY$122154 IWG PLC 13 13 10 481.8 481.7 422 497 6 473 18 0
15 00604574 BARRATT DEVELOPMENTS P L C 14 17 587 481.1 473.6 31 530 9 446 75 0
16 06035106 FRASERS GROUP PLC 15 16 2982 480.1 474.8 14 484 2 438 44 0
17 GRZEGORZ$NA$SZEWCZYK$1985$7 GRZEGORZ SZEWCZYK 16 14 8 480 480 480 481 1 480 0 0
18 DARREN$NA$SYMES$1958$10 DARREN SYMES 17 15 9 475.5 475.5 474.5 478 2 475 1 0
19 08885072 PETS AT HOME GROUP PLC 18 19 1226949 468 389.1 1 770 216 514 40 0
20 10657226 BGF GROUP PLC 19 23 6219 462.1 343 10 674 99 378 197 0
21 03981143 OCTOPUS CAPITAL LIMITED 20 18 1624 414.5 411.7 19 431 4 310 117 0
22 11444019 M&G PLC 21 20 17408 404 386.6 6 469 14 298 157 0
23 00102498 BP P.L.C. 22 26 1757 377.8 336.4 18 493 5 390 96 2
24 10510800 IVC ACQUISITION PIKCO LTD 23 21 1535931 370 366.3 1 371 1 341 29 0
25 SUN LIFE FINANCIAL INC.$CANADA$F380 SUN LIFE FINANCIAL INC. 24 22 2086664 364.7 358.2 1 469 10 242 217 0
26 03777037 PLACES FOR PEOPLE GROUP LIMITED 25 25 458 345.8 338.7 35.5 387 11 324 52 0
27 KANE$STEVEN JAMES$WALLACE$1988$4 KANE WALLACE 26 24 12 342 342 342 343 1 342 0 0
28 01417162 LEGAL & GENERAL GROUP PLC 27 28 3477 333.1 321 13 399 14 286 99 0
29 04569346 DIGNITY PLC 28 27 45566 332.9 328.5 4 348 13 284 51 0
30 02468686 AVIVA PLC 29 29 58547 316.1 305.8 4 372 11 261 100 0
31 00621920 BRITISH LAND COMPANY PUBLIC LIMITED COMPANY(THE) 30 30 11060 301.8 295.8 7.5 315 1 218 96 0
32 01142830 3I GROUP PLC 31 35 1948 290.6 276.4 17.3 392 12 176 204 0
33 00296805 TAYLOR WIMPEY PLC 32 33 6642 289.9 283.3 9.5 339 11 260 68 0
34 00082548 REACH PLC 33 31 365 289.4 286.7 39 297 1 229 67 0
35 BRYAN$ANTHONY$THORNTON$1955$7 BRYAN THORNTON 34 32 135 287.3 284.3 70 299 6 290 3 0
36 08286875 WPP JUBILEE LIMITED 35 36 268 284.8 271.2 45.8 314 6 200 108 0
37 RONALD$TERENCE$RICHARDS$1945$1 RONALD RICHARDS 36 34 17 280 280 280 281 1 280 0 0
38 02877315 REDROW PLC 37 37 176901 273.2 269.7 2 292 5 268 19 0
39 WOODLEY$LARKIN$HUNT$1945$11 WOODLEY HUNT 38 39 1331918 261.3 256.5 1 287 2 154 131 0
40 HANNOVER RUCK SE$GERMANY$HRB 6778 HANNOVER RUCK SE 39 38 82217 261 258.4 3 262 1 254 7 0
41 01470151 BAE SYSTEMS PLC 40 42 387 252.9 251.4 38 301 7 206 88 0
42 ANDREW$ROY$LEIGHTON$1949$10 ANDREW LEIGHTON 41 41 38 252.3 251.4 159.3 256 3 251 2 0
43 08340090 COUNTRYWIDE LIMITED 42 43 785896 248 245.5 1 249 1 217 31 0
44 04967001 ITV PLC 43 46 71002 247.9 242.3 3.2 274 16 209 49 0
45 10763268 CSC FINANCIAL SERVICES HOLDINGS LIMITED 44 44 306820 247.7 245 2 250 1 161 88 0
46 HEIDELBERGCEMENT AG$GERMANY$HRB 33082 HEIDELBERGCEMENT AG 45 48 210440 246.4 236.1 2 260 3 166 91 0
47 STEPHEN$ALLEN$SCHWARZMAN$1947$2 STEPHEN SCHWARZMAN 46 45 96 244.7 243.4 90 256 3 171 82 0
48 OC301825 HGCAPITAL LLP 47 47 2009 242.2 239.1 17 247 4 164 79 0
49 OC360196 EQUISTONE LLP 48 40 242598 241.6 252.4 2 261 4 167 90 0
50 03140521 MATTIOLI WOODS PLC 49 55 453 241.1 226.6 35.5 290 22 181 87 0
51 STEPHEN$STUART SOLOMON$CONWAY$1948$2 STEPHEN CONWAY 50 49 5851 237.5 233.6 10 317 14 230 73 0
52 CRH PLC$IRELAND$12965 CRH PLC 51 50 617583 235.4 230.1 1 268 7 201 60 0
53 OC332179 DRUCES LLP 52 52 183094 230.3 227.7 2 234 3 229 2 0
54 BELLWAY P.L.C.$ENGLAND$1372603 BELLWAY P.L.C. 53 53 1279 229.5 227.3 21 253 4 236 13 0
55 SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED 54 51 961566 229.2 229.5 1 270 4 151 115 0
56 MICHAEL$JOHN$HALL$1971$7 MICHAEL HALL 55 54 22 225.3 226.9 226.8 239 5 234 0 0
57 00521970 MORGAN SINDALL GROUP PLC 56 61 969 217.9 209.6 24 298 16 205 77 0
58 BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4 BENZION FRESHWATER 57 56 1526 215.6 216.4 19.5 257 6 222 29 0
59 MICHAEL$BARRY$TABOR$1941$10 MICHAEL TABOR 58 60 194884 214.8 211.1 2 226 4 161 61 0
60 00306718 VISTRY GROUP PLC 59 59 173704 213.8 211.2 2 260 7 223 30 0
61 SC045551 NATWEST GROUP PLC 60 58 42589 213.6 211.5 4 261 8 173 79 1
62 06397765 OCTOPUS TITAN VCT PLC 61 62 11088 211.1 208.7 7.5 221 4 124 93 0
63 RADOVAN$NA$KOLJEVIC$1967$5 RADOVAN KOLJEVIC 62 63 47760 211 208.4 4 216 4 204 8 0
64 05172586 THE BERKELEY GROUP HOLDINGS PLC 63 64 619407 209.2 207.2 1 216 1 202 13 0
65 SENTTHURAN$NA$NADARAJAH$1979$11 SENTTHURAN NADARAJAH 64 66 3685 207 205.1 13 208 1 206 1 0
66 JOAQUIM$NA$MAGRO DE ALMEIDA$1949$1 JOAQUIM MAGRO DE ALMEIDA 65 65 27 205.8 205.5 205.5 216 4 212 0 0
67 OLUWOLE$NA$KOLADE$1966$11 OLUWOLE KOLADE 66 70 57071 204.4 197.2 4 235 10 97 128 0
68 DAVID$JAMES$BARRICK$1984$1 DAVID BARRICK 67 57 25 201 213.5 213.6 254 1 251 2 0
69 STACEY$LOUISE$TRAMASEUR$1997$1 STACEY TRAMASEUR 68 67 29 201 201 201 202 1 201 0 0
70 ROMY$ELIZABETH$SUMMERSKILL$1967$1 ROMY SUMMERSKILL 69 68 15243 200.9 199.1 6.5 217 2 142 73 0
71 JAY$NA$THOMAS$1981$1 JAY THOMAS 70 69 30 199 199 199 200 1 199 0 0
72 SC286832 ABRDN PLC 71 74 1623 194 189.6 19 204 5 157 42 0
73 04120344 WHITBREAD PLC 72 71 592751 193.5 191 1 200 3 170 27 0
74 KEITH$NA$BRESLAUER$1966$3 KEITH BRESLAUER 73 72 71852 192.9 190.1 3 200 2 131 67 0
75 OC313101 AUGUST EQUITY LLP 74 73 5699 191.8 189.7 10 194 2 97 92 3
76 PATRICK$ANTHONY$MCKENNA$1956$6 PATRICK MCKENNA 75 79 13432 185 182.9 7 197 4 167 26 0
77 GUY$NA$HANDS$1959$8 GUY HANDS 76 77 3793 183.4 183.9 12.5 203 3 157 43 0
78 REBECCA$LOUISE$CODY$1997$7 REBECCA CODY 77 80 33 182 182 182 183 1 182 0 0
79 JEAN-GUY$NA$DESJARDINS$1944$10 JEAN-GUY DESJARDINS 78 88 9585 180.7 165.9 8 298 12 208 78 0
80 00445790 TESCO PLC 79 82 1527 180.4 178.2 19.5 199 4 132 63 0
81 STEPHEN$JAMES$ROBERTSON$1960$3 STEPHEN ROBERTSON 80 76 156655 178.2 186.6 2.3 383 14 269 100 0
82 MANJIT$NA$DALE$1965$6 MANJIT DALE 81 92 162072 178.2 163.9 2.3 383 14 269 100 0
83 THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064 THE BERKELEY GROUP PLC 82 81 381 177.4 178.2 38.5 208 2 165 41 0
84 MOHAMMED$NA$AYYAZ$1996$12 MOHAMMED AYYAZ 83 83 35 177.3 177.3 177.3 222 30 192 0 0
85 CERI$NA$JOHN$1955$7 CERI JOHN 84 84 36 176 176 176 177 1 176 0 0
86 04330127 WILMINGTON TRUST (UK) LIMITED 85 85 185351 174.7 172.4 2 180 2 123 55 0
87 08379990 LIBERTY GLOBAL PLC 86 96 4578 172.6 162.3 11.5 335 11 239 85 0
88 VISTRY (JERSEY) LIMITED$JERSEY$130175 VISTRY (JERSEY) LIMITED 87 99 672013 171.8 161.5 1 243 10 186 47 0
89 07934492 CURTIS BANKS GROUP PLC 88 87 9563 170.8 168.2 8 181 4 161 16 0
90 00617987 HSBC HOLDINGS PLC 89 102 2511 170.8 160.2 15.2 220 6 150 64 0
91 BROOKFIELD ASSET MANAGEMENT INC$CANADA$/ BROOKFIELD ASSET MANAGEMENT INC 90 75 555776 170.5 186.6 1 347 4 225 118 0
92 QATAR INVESTMENT AUTHORITY$QATAR$/ QATAR INVESTMENT AUTHORITY 91 114 2818663 170.5 150.9 1 347 4 225 118 0
93 06394563 ENDEMOL SHINE GROUP HOLDING UK LIMITED 92 86 78751 170 168.3 3 175 3 142 30 0
94 OC333409 TRICOR SERVICES EUROPE LLP 93 91 42092 169.8 164.1 4 221 21 159 41 0
95 SOFTBANK GROUP CORP$JAPAN$0104-01-056795 SOFTBANK GROUP CORP 94 93 80640 168.7 163.8 3 181 5 101 75 0
96 07023200 ADP PRIMARY CARE SERVICES LIMITED 95 89 962994 167.7 165.8 1 170 1 134 35 0
97 03199160 THE UNITE GROUP PLC 96 94 42466 164.3 162.7 4 168 2 134 32 0
98 11499533 SCOOBY BIDCO LIMITED 97 97 1443396 163.9 162.2 1 172 3 143 26 0
99 00349201 ST. MODWEN PROPERTIES PLC 98 90 195 162.4 164.7 56 200 6 164 30 0
100 11606773 PHOENIX GROUP HOLDINGS PLC 99 98 93217 161.8 162.1 3 177 3 134 40 0
101 ANDRZEJ$NA$NIEMYJSKI$1975$11 ANDRZEJ NIEMYJSKI 100 100 37 161.5 161.5 161.5 164 2 162 0 0

101
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@ -0,0 +1,101 @@
participant_id,sumdpi,rankdpi,sumnpi,ranknpi,sumtransitive,ranktransitive,diff_npi_dpi,diff_transitive_dpi,diff_transitive_npi
SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624,4,42441,1452.95022222222,1,1482.18842011308,1,1448.95022222222,1478.18842011308,29.2381978908597
ANDREW$SIMON$DAVIS$1963$7,14.5042,2788,869.487555555556,6,881.3365356159,5,854.983355555556,866.8323356159,11.8489800603431
SC095000,5,24872,670.525666666667,8,735.610780469834,7,665.525666666667,730.610780469834,65.0851138031673
READE$NA$GRIFFITH$1965$4,1.4972,491331,636.465111111111,9,657.49955601355,10,634.967911111111,656.00235601355,21.0344449024385
11443992,11,5149,591.460888888889,10,669.338549583877,9,580.460888888889,658.338549583877,77.8776606949871
PERSIMMON PLC$ENGLAND$1818486,14,2911,578.420555555556,11,586.035982151633,11,564.420555555556,572.035982151633,7.6154265960771
INTERTRUST N.V.$THE NETHERLANDS$N/A,1,887094,511.782222222222,12,519.652355682228,12,510.782222222222,518.652355682228,7.87013346000617
06035106,14,2982,474.829444444445,16,480.114910906034,15,460.829444444445,466.114910906034,5.28546646158912
00604574,31,587,473.602,17,481.125633609192,14,442.602,450.125633609192,7.5236336091923
03981143,19,1624,411.697111111111,18,414.491202616254,20,392.697111111111,395.491202616254,2.79409150514357
08885072,1,1226949,389.079222222222,19,468.031302647188,18,388.079222222222,467.031302647188,78.9520804249655
11444019,6,17408,386.593444444445,20,403.985152490125,21,380.593444444445,397.985152490125,17.3917080456807
10510800,1,1535931,366.270333333333,21,370,23,365.270333333333,369,3.72966666666673
SUN LIFE FINANCIAL INC.$CANADA$F380,1,2086664,358.225444444444,22,364.651221643269,24,357.225444444444,363.651221643269,6.42577719882496
10657226,10,6219,342.955333333334,23,462.050947342302,19,332.955333333334,452.050947342302,119.095614008968
04569346,4,45566,328.479,27,332.883401968393,28,324.479,328.883401968393,4.40440196839307
00102498,18,1757,336.391666666667,26,377.785641323169,22,318.391666666667,359.785641323169,41.3939746565019
01417162,13,3477,320.993555555555,28,333.114660129009,27,307.993555555555,320.114660129009,12.121104573454
03777037,35.4911,458,338.669111111111,25,345.770230509207,25,303.178011111111,310.279130509207,7.10111939809553
02468686,3.9928,58547,305.836888888889,29,316.091281388984,29,301.844088888889,312.098481388984,10.2543925000952
00621920,7.5086,11060,295.787333333333,30,301.826105187632,30,288.278733333333,294.317505187632,6.03877185429838
00296805,9.5097,6642,283.340333333333,33,289.902171627357,32,273.830633333333,280.392471627357,6.56183829402386
02877315,2,176901,269.693888888889,37,273.241267886102,37,267.693888888889,271.241267886102,3.54737899721323
01142830,17.3204,1948,276.395222222222,35,290.62995167509,31,259.074822222222,273.30955167509,14.2347294528681
WOODLEY$LARKIN$HUNT$1945$11,1,1331918,256.523555555556,39,261.339361555954,38,255.523555555556,260.339361555954,4.81580600039837
HANNOVER RUCK SE$GERMANY$HRB 6778,3,82217,258.389888888889,38,261,39,255.389888888889,258,2.61011111111122
OC360196,2,242598,252.407222222222,40,241.635711925833,48,250.407222222222,239.635711925833,-10.7715102963891
00082548,39,365,286.73,31,289.415186936244,33,247.73,250.415186936244,2.68518693624372
08340090,1,785896,245.526666666667,43,248,42,244.526666666667,247,2.47333333333344
10763268,2,306820,245.016666666667,44,247.665776742879,44,243.016666666667,245.665776742879,2.6491100762122
04967001,3.1677,71002,242.283111111111,46,247.855191284282,43,239.115411111111,244.687491284282,5.57208017317043
HEIDELBERGCEMENT AG$GERMANY$HRB 33082,2,210440,236.095777777778,48,246.443097797991,45,234.095777777778,244.443097797991,10.3473200202133
CRH PLC$IRELAND$12965,1,617583,230.075888888889,50,235.350874688043,51,229.075888888889,234.350874688043,5.27498579915408
SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA,1,961566,229.452111111111,51,229.246004751229,54,228.452111111111,228.246004751229,-0.206106359882426
OC332179,2,183094,227.677555555556,52,230.332888592395,52,225.677555555556,228.332888592395,2.65533303683935
08286875,45.8382,268,271.165444444445,36,284.837428399735,35,225.327244444445,238.999228399736,13.6719839552909
STEPHEN$STUART SOLOMON$CONWAY$1948$2,10,5851,233.584888888889,49,237.537965323381,50,223.584888888889,227.537965323381,3.95307643449249
OC301825,17,2009,239.057666666667,47,242.212988425641,47,222.057666666667,225.212988425641,3.15532175897408
BRYAN$ANTHONY$THORNTON$1955$7,69.9992,135,284.260888888889,32,287.332221480987,34,214.261688888889,217.333021480987,3.07133259209854
01470151,38,387,251.364888888889,42,252.900520102143,40,213.364888888889,214.900520102143,1.53563121325368
00306718,2,173704,211.167444444445,59,213.813343161875,59,209.167444444445,211.813343161875,2.64589871743056
MICHAEL$BARRY$TABOR$1941$10,2,194884,211.140666666667,60,214.829760965527,58,209.140666666667,212.829760965527,3.68909429886025
SC045551,4,42589,211.497,58,213.557523551435,60,207.497,209.557523551435,2.06052355143524
BELLWAY P.L.C.$ENGLAND$1372603,21,1279,227.340222222222,53,229.460570633214,53,206.340222222222,208.460570633214,2.12034841099197
05172586,1,619407,207.170222222222,64,209.167889557863,63,206.170222222222,208.167889557863,1.99766733564073
RADOVAN$NA$KOLJEVIC$1967$5,4,47760,208.412777777778,63,210.999332888592,62,204.412777777778,206.999332888592,2.58655511081454
06397765,7.5069,11088,208.652111111111,62,211.130367917775,61,201.145211111111,203.623467917775,2.47825680666418
BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4,19.5484,1526,216.430333333333,56,215.557869788565,57,196.881933333333,196.009469788565,-0.872463544768436
OLUWOLE$NA$KOLADE$1966$11,4,57071,197.168333333333,70,204.402107259893,66,193.168333333333,200.402107259893,7.23377392655939
ROMY$ELIZABETH$SUMMERSKILL$1967$1,6.5042,15243,199.066222222222,68,200.878082442063,69,192.562022222222,194.373882442063,1.81186021984072
SENTTHURAN$NA$NADARAJAH$1979$11,13,3685,205.072666666667,66,207,64,192.072666666667,194,1.92733333333339
03140521,35.5041,453,226.638222222222,55,241.120645742615,49,191.134122222222,205.616545742615,14.4824235203928
04120344,1,592751,191.048666666667,71,193.500249906766,72,190.048666666667,192.500249906766,2.45158324009947
KEITH$NA$BRESLAUER$1966$3,3.0098,71852,190.085222222222,72,192.94594185951,73,187.075422222222,189.93614185951,2.86071963728801
BROOKFIELD ASSET MANAGEMENT INC$CANADA$/,1.0136,555776,186.598,75,170.469159583876,90,185.5844,169.455559583876,-16.1288404161239
00521970,24,969,209.580444444445,61,217.943276147564,56,185.580444444444,193.943276147564,8.3628317031195
STEPHEN$JAMES$ROBERTSON$1960$3,2.3488,156655,186.561666666667,76,178.248028826349,80,184.212866666667,175.899228826349,-8.31363784031754
TIMOTHY$PATRICK CAMROUX$OLIVER$1944$3,0.2488,3911463,183.432777777778,78,150.791367871721,113,183.183977777778,150.542567871721,-32.6414099060569
OC313101,10.0091,5699,189.673777777778,73,191.798555400488,74,179.664677777778,181.789455400488,2.12477762271021
PATRICK$ANTHONY$MCKENNA$1956$6,7,13432,182.905444444444,79,184.950746253802,75,175.905444444444,177.950746253802,2.04530180935731
GUY$NA$HANDS$1959$8,12.5038,3793,183.917666666667,77,183.377417210637,76,171.413866666667,170.873617210637,-0.540249456029898
SC286832,19,1623,189.588777777778,74,194.009419943477,71,170.588777777778,175.009419943477,4.42064216569923
04330127,2,185351,172.353,85,174.666277436318,85,170.353,172.666277436318,2.31327743631806
06394563,3,78751,168.266,86,170.02573434901,92,165.266,167.02573434901,1.75973434901024
07023200,1,962994,165.817333333333,89,167.665219974605,95,164.817333333333,166.665219974605,1.84788664127171
MANJIT$NA$DALE$1965$6,2.3176,162072,163.911666666667,92,178.248028826349,81,161.594066666667,175.930428826349,14.3363621596826
CHARLES$GUY$CAMROUX-OLIVER$1970$4,1.2452,551192,162.649666666667,95,151.791367871721,110,161.404466666667,150.546167871721,-10.8582987949457
11499533,1,1443396,162.169888888889,97,163.898038919407,97,161.169888888889,162.898038919407,1.72815003051784
SOFTBANK GROUP CORP$JAPAN$0104-01-056795,3,80640,163.836444444444,93,168.66025626587,94,160.836444444444,165.66025626587,4.82381182142512
VISTRY (JERSEY) LIMITED$JERSEY$130175,1,672013,161.530777777778,99,171.767151202623,87,160.530777777778,170.767151202623,10.2363734248455
07934492,8,9563,168.187111111111,87,170.819869720549,88,160.187111111111,162.819869720549,2.63275860943807
OC333409,4,42092,164.090222222222,91,169.773887544448,93,160.090222222222,165.773887544448,5.68366532222564
11606773,3,93217,162.071444444444,98,161.809404862073,99,159.071444444444,158.809404862073,-0.262039582371528
03199160,4,42466,162.718555555556,94,164.33318506947,96,158.718555555556,160.33318506947,1.61462951391485
00445790,19.5101,1527,178.167555555556,82,180.399232361494,79,158.657455555556,160.889132361494,2.23167680593886
02708030,2,179758,160.509555555556,101,161.051230246867,101,158.509555555556,159.051230246867,0.54167469131167
JEAN-GUY$NA$DESJARDINS$1944$10,8,9585,165.875,88,180.731962006548,78,157.875,172.731962006548,14.8569620065477
CASTLE BIDCO LIMITED$UNITED KINGDOM$5988526,1,609460,157.867666666667,105,158.345681428497,104,156.867666666667,157.345681428497,0.478014761829996
SEAN$MICHAEL$DINNEN$1968$3,1,2659434,157.004444444444,106,158.573288802633,103,156.004444444444,157.573288802633,1.56884435818873
STEPHEN$ALLEN$SCHWARZMAN$1947$2,90,96,243.444333333333,45,244.6992587951,46,153.444333333333,154.6992587951,1.25492546176619
THE BRITISH UNITED PROVIDENT ASSOCIATION LIMITED$ENGLAND$432511,1,656307,154.393222222222,108,155.868768815271,106,153.393222222222,154.868768815271,1.47554659304876
"LENDLEASE INTERNATIONAL PTY LIMITED$NEW SOUTH WALES, AUSTRALIA$000489109",1,649756,151.971666666667,112,93.8837570262932,251,150.971666666667,92.8837570262932,-58.0879096403735
OC329299,7,13415,157.924333333333,104,153.688376714201,109,150.924333333333,146.688376714201,-4.23595661913217
08379990,11.4977,4578,162.343222222222,96,172.558543709203,86,150.845522222222,161.060843709203,10.2153214869812
QATAR INVESTMENT AUTHORITY$QATAR$/,0.9864,2818663,150.943333333333,114,170.469159583876,91,149.956933333333,169.482759583876,19.5258262505427
IMRAN$NA$HAKIM$1977$9,4.6661,33921,154.101666666667,110,158.30270905129,105,149.435566666667,153.63660905129,4.20104238462346
BRIDGEPOINT EUROPE (SGP) LIMITED$SCOTLAND$SC332267,5.5008,22630,154.380333333333,109,95.1858779163316,247,148.879533333333,89.6850779163316,-59.1944554170018
00293262,1,594882,148.146333333333,117,150.022282279097,114,147.146333333333,149.022282279097,1.87594894576387
THE LEADERS ROMANS MIDCO2 LIMITED$ENGLAND$9939213,1,1399100,147.481333333333,118,149,116,146.481333333333,148,1.51866666666672
00617987,15.2227,2511,160.153666666667,102,170.760746414119,89,144.930966666667,155.538046414119,10.6070797474518
MARK$DAVID$STOTT$1972$4,8,9812,151.257777777778,113,148.326943547396,119,143.257777777778,140.326943547396,-2.93083423038166
08669482,6.507,15133,149.444111111111,116,148.622813846579,117,142.937111111111,142.115813846579,-0.821297264532518
OC301604,9.5009,6764,150.549333333333,115,147.836555181346,120,141.048433333333,138.335655181346,-2.71277815198775
00998314,18.9966,1677,159.077,103,160,102,140.0804,141.0034,0.922999999999945
THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064,38.4924,381,178.171555555556,81,177.436350655372,82,139.679155555556,138.943950655372,-0.73520490018322
03942129,7,12849,146.559666666667,119,148.500250109757,118,139.559666666667,141.500250109757,1.94058344308993
04369054,2,211643,141.481333333333,129,143.298790128817,125,139.481333333333,141.298790128817,1.81745679548422
ALISTAIR$NA$STEELE$1953$11,6,20851,144.591888888889,121,146,121,138.591888888889,140,1.40811111111108
SEGRO PLC$ENGLAND AND WALES$167591,3.4979,65636,139.189555555556,133,140.16761135978,133,135.691655555556,136.66971135978,0.978055804224397
OC319972,5.8467,21435,140.911888888889,130,142.333333333333,128,135.065188888889,136.486633333333,1.42144444444446
1 participant_id sumdpi rankdpi sumnpi ranknpi sumtransitive ranktransitive diff_npi_dpi diff_transitive_dpi diff_transitive_npi
2 SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624 4 42441 1452.95022222222 1 1482.18842011308 1 1448.95022222222 1478.18842011308 29.2381978908597
3 ANDREW$SIMON$DAVIS$1963$7 14.5042 2788 869.487555555556 6 881.3365356159 5 854.983355555556 866.8323356159 11.8489800603431
4 SC095000 5 24872 670.525666666667 8 735.610780469834 7 665.525666666667 730.610780469834 65.0851138031673
5 READE$NA$GRIFFITH$1965$4 1.4972 491331 636.465111111111 9 657.49955601355 10 634.967911111111 656.00235601355 21.0344449024385
6 11443992 11 5149 591.460888888889 10 669.338549583877 9 580.460888888889 658.338549583877 77.8776606949871
7 PERSIMMON PLC$ENGLAND$1818486 14 2911 578.420555555556 11 586.035982151633 11 564.420555555556 572.035982151633 7.6154265960771
8 INTERTRUST N.V.$THE NETHERLANDS$N/A 1 887094 511.782222222222 12 519.652355682228 12 510.782222222222 518.652355682228 7.87013346000617
9 06035106 14 2982 474.829444444445 16 480.114910906034 15 460.829444444445 466.114910906034 5.28546646158912
10 00604574 31 587 473.602 17 481.125633609192 14 442.602 450.125633609192 7.5236336091923
11 03981143 19 1624 411.697111111111 18 414.491202616254 20 392.697111111111 395.491202616254 2.79409150514357
12 08885072 1 1226949 389.079222222222 19 468.031302647188 18 388.079222222222 467.031302647188 78.9520804249655
13 11444019 6 17408 386.593444444445 20 403.985152490125 21 380.593444444445 397.985152490125 17.3917080456807
14 10510800 1 1535931 366.270333333333 21 370 23 365.270333333333 369 3.72966666666673
15 SUN LIFE FINANCIAL INC.$CANADA$F380 1 2086664 358.225444444444 22 364.651221643269 24 357.225444444444 363.651221643269 6.42577719882496
16 10657226 10 6219 342.955333333334 23 462.050947342302 19 332.955333333334 452.050947342302 119.095614008968
17 04569346 4 45566 328.479 27 332.883401968393 28 324.479 328.883401968393 4.40440196839307
18 00102498 18 1757 336.391666666667 26 377.785641323169 22 318.391666666667 359.785641323169 41.3939746565019
19 01417162 13 3477 320.993555555555 28 333.114660129009 27 307.993555555555 320.114660129009 12.121104573454
20 03777037 35.4911 458 338.669111111111 25 345.770230509207 25 303.178011111111 310.279130509207 7.10111939809553
21 02468686 3.9928 58547 305.836888888889 29 316.091281388984 29 301.844088888889 312.098481388984 10.2543925000952
22 00621920 7.5086 11060 295.787333333333 30 301.826105187632 30 288.278733333333 294.317505187632 6.03877185429838
23 00296805 9.5097 6642 283.340333333333 33 289.902171627357 32 273.830633333333 280.392471627357 6.56183829402386
24 02877315 2 176901 269.693888888889 37 273.241267886102 37 267.693888888889 271.241267886102 3.54737899721323
25 01142830 17.3204 1948 276.395222222222 35 290.62995167509 31 259.074822222222 273.30955167509 14.2347294528681
26 WOODLEY$LARKIN$HUNT$1945$11 1 1331918 256.523555555556 39 261.339361555954 38 255.523555555556 260.339361555954 4.81580600039837
27 HANNOVER RUCK SE$GERMANY$HRB 6778 3 82217 258.389888888889 38 261 39 255.389888888889 258 2.61011111111122
28 OC360196 2 242598 252.407222222222 40 241.635711925833 48 250.407222222222 239.635711925833 -10.7715102963891
29 00082548 39 365 286.73 31 289.415186936244 33 247.73 250.415186936244 2.68518693624372
30 08340090 1 785896 245.526666666667 43 248 42 244.526666666667 247 2.47333333333344
31 10763268 2 306820 245.016666666667 44 247.665776742879 44 243.016666666667 245.665776742879 2.6491100762122
32 04967001 3.1677 71002 242.283111111111 46 247.855191284282 43 239.115411111111 244.687491284282 5.57208017317043
33 HEIDELBERGCEMENT AG$GERMANY$HRB 33082 2 210440 236.095777777778 48 246.443097797991 45 234.095777777778 244.443097797991 10.3473200202133
34 CRH PLC$IRELAND$12965 1 617583 230.075888888889 50 235.350874688043 51 229.075888888889 234.350874688043 5.27498579915408
35 SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA 1 961566 229.452111111111 51 229.246004751229 54 228.452111111111 228.246004751229 -0.206106359882426
36 OC332179 2 183094 227.677555555556 52 230.332888592395 52 225.677555555556 228.332888592395 2.65533303683935
37 08286875 45.8382 268 271.165444444445 36 284.837428399735 35 225.327244444445 238.999228399736 13.6719839552909
38 STEPHEN$STUART SOLOMON$CONWAY$1948$2 10 5851 233.584888888889 49 237.537965323381 50 223.584888888889 227.537965323381 3.95307643449249
39 OC301825 17 2009 239.057666666667 47 242.212988425641 47 222.057666666667 225.212988425641 3.15532175897408
40 BRYAN$ANTHONY$THORNTON$1955$7 69.9992 135 284.260888888889 32 287.332221480987 34 214.261688888889 217.333021480987 3.07133259209854
41 01470151 38 387 251.364888888889 42 252.900520102143 40 213.364888888889 214.900520102143 1.53563121325368
42 00306718 2 173704 211.167444444445 59 213.813343161875 59 209.167444444445 211.813343161875 2.64589871743056
43 MICHAEL$BARRY$TABOR$1941$10 2 194884 211.140666666667 60 214.829760965527 58 209.140666666667 212.829760965527 3.68909429886025
44 SC045551 4 42589 211.497 58 213.557523551435 60 207.497 209.557523551435 2.06052355143524
45 BELLWAY P.L.C.$ENGLAND$1372603 21 1279 227.340222222222 53 229.460570633214 53 206.340222222222 208.460570633214 2.12034841099197
46 05172586 1 619407 207.170222222222 64 209.167889557863 63 206.170222222222 208.167889557863 1.99766733564073
47 RADOVAN$NA$KOLJEVIC$1967$5 4 47760 208.412777777778 63 210.999332888592 62 204.412777777778 206.999332888592 2.58655511081454
48 06397765 7.5069 11088 208.652111111111 62 211.130367917775 61 201.145211111111 203.623467917775 2.47825680666418
49 BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4 19.5484 1526 216.430333333333 56 215.557869788565 57 196.881933333333 196.009469788565 -0.872463544768436
50 OLUWOLE$NA$KOLADE$1966$11 4 57071 197.168333333333 70 204.402107259893 66 193.168333333333 200.402107259893 7.23377392655939
51 ROMY$ELIZABETH$SUMMERSKILL$1967$1 6.5042 15243 199.066222222222 68 200.878082442063 69 192.562022222222 194.373882442063 1.81186021984072
52 SENTTHURAN$NA$NADARAJAH$1979$11 13 3685 205.072666666667 66 207 64 192.072666666667 194 1.92733333333339
53 03140521 35.5041 453 226.638222222222 55 241.120645742615 49 191.134122222222 205.616545742615 14.4824235203928
54 04120344 1 592751 191.048666666667 71 193.500249906766 72 190.048666666667 192.500249906766 2.45158324009947
55 KEITH$NA$BRESLAUER$1966$3 3.0098 71852 190.085222222222 72 192.94594185951 73 187.075422222222 189.93614185951 2.86071963728801
56 BROOKFIELD ASSET MANAGEMENT INC$CANADA$/ 1.0136 555776 186.598 75 170.469159583876 90 185.5844 169.455559583876 -16.1288404161239
57 00521970 24 969 209.580444444445 61 217.943276147564 56 185.580444444444 193.943276147564 8.3628317031195
58 STEPHEN$JAMES$ROBERTSON$1960$3 2.3488 156655 186.561666666667 76 178.248028826349 80 184.212866666667 175.899228826349 -8.31363784031754
59 TIMOTHY$PATRICK CAMROUX$OLIVER$1944$3 0.2488 3911463 183.432777777778 78 150.791367871721 113 183.183977777778 150.542567871721 -32.6414099060569
60 OC313101 10.0091 5699 189.673777777778 73 191.798555400488 74 179.664677777778 181.789455400488 2.12477762271021
61 PATRICK$ANTHONY$MCKENNA$1956$6 7 13432 182.905444444444 79 184.950746253802 75 175.905444444444 177.950746253802 2.04530180935731
62 GUY$NA$HANDS$1959$8 12.5038 3793 183.917666666667 77 183.377417210637 76 171.413866666667 170.873617210637 -0.540249456029898
63 SC286832 19 1623 189.588777777778 74 194.009419943477 71 170.588777777778 175.009419943477 4.42064216569923
64 04330127 2 185351 172.353 85 174.666277436318 85 170.353 172.666277436318 2.31327743631806
65 06394563 3 78751 168.266 86 170.02573434901 92 165.266 167.02573434901 1.75973434901024
66 07023200 1 962994 165.817333333333 89 167.665219974605 95 164.817333333333 166.665219974605 1.84788664127171
67 MANJIT$NA$DALE$1965$6 2.3176 162072 163.911666666667 92 178.248028826349 81 161.594066666667 175.930428826349 14.3363621596826
68 CHARLES$GUY$CAMROUX-OLIVER$1970$4 1.2452 551192 162.649666666667 95 151.791367871721 110 161.404466666667 150.546167871721 -10.8582987949457
69 11499533 1 1443396 162.169888888889 97 163.898038919407 97 161.169888888889 162.898038919407 1.72815003051784
70 SOFTBANK GROUP CORP$JAPAN$0104-01-056795 3 80640 163.836444444444 93 168.66025626587 94 160.836444444444 165.66025626587 4.82381182142512
71 VISTRY (JERSEY) LIMITED$JERSEY$130175 1 672013 161.530777777778 99 171.767151202623 87 160.530777777778 170.767151202623 10.2363734248455
72 07934492 8 9563 168.187111111111 87 170.819869720549 88 160.187111111111 162.819869720549 2.63275860943807
73 OC333409 4 42092 164.090222222222 91 169.773887544448 93 160.090222222222 165.773887544448 5.68366532222564
74 11606773 3 93217 162.071444444444 98 161.809404862073 99 159.071444444444 158.809404862073 -0.262039582371528
75 03199160 4 42466 162.718555555556 94 164.33318506947 96 158.718555555556 160.33318506947 1.61462951391485
76 00445790 19.5101 1527 178.167555555556 82 180.399232361494 79 158.657455555556 160.889132361494 2.23167680593886
77 02708030 2 179758 160.509555555556 101 161.051230246867 101 158.509555555556 159.051230246867 0.54167469131167
78 JEAN-GUY$NA$DESJARDINS$1944$10 8 9585 165.875 88 180.731962006548 78 157.875 172.731962006548 14.8569620065477
79 CASTLE BIDCO LIMITED$UNITED KINGDOM$5988526 1 609460 157.867666666667 105 158.345681428497 104 156.867666666667 157.345681428497 0.478014761829996
80 SEAN$MICHAEL$DINNEN$1968$3 1 2659434 157.004444444444 106 158.573288802633 103 156.004444444444 157.573288802633 1.56884435818873
81 STEPHEN$ALLEN$SCHWARZMAN$1947$2 90 96 243.444333333333 45 244.6992587951 46 153.444333333333 154.6992587951 1.25492546176619
82 THE BRITISH UNITED PROVIDENT ASSOCIATION LIMITED$ENGLAND$432511 1 656307 154.393222222222 108 155.868768815271 106 153.393222222222 154.868768815271 1.47554659304876
83 LENDLEASE INTERNATIONAL PTY LIMITED$NEW SOUTH WALES, AUSTRALIA$000489109 1 649756 151.971666666667 112 93.8837570262932 251 150.971666666667 92.8837570262932 -58.0879096403735
84 OC329299 7 13415 157.924333333333 104 153.688376714201 109 150.924333333333 146.688376714201 -4.23595661913217
85 08379990 11.4977 4578 162.343222222222 96 172.558543709203 86 150.845522222222 161.060843709203 10.2153214869812
86 QATAR INVESTMENT AUTHORITY$QATAR$/ 0.9864 2818663 150.943333333333 114 170.469159583876 91 149.956933333333 169.482759583876 19.5258262505427
87 IMRAN$NA$HAKIM$1977$9 4.6661 33921 154.101666666667 110 158.30270905129 105 149.435566666667 153.63660905129 4.20104238462346
88 BRIDGEPOINT EUROPE (SGP) LIMITED$SCOTLAND$SC332267 5.5008 22630 154.380333333333 109 95.1858779163316 247 148.879533333333 89.6850779163316 -59.1944554170018
89 00293262 1 594882 148.146333333333 117 150.022282279097 114 147.146333333333 149.022282279097 1.87594894576387
90 THE LEADERS ROMANS MIDCO2 LIMITED$ENGLAND$9939213 1 1399100 147.481333333333 118 149 116 146.481333333333 148 1.51866666666672
91 00617987 15.2227 2511 160.153666666667 102 170.760746414119 89 144.930966666667 155.538046414119 10.6070797474518
92 MARK$DAVID$STOTT$1972$4 8 9812 151.257777777778 113 148.326943547396 119 143.257777777778 140.326943547396 -2.93083423038166
93 08669482 6.507 15133 149.444111111111 116 148.622813846579 117 142.937111111111 142.115813846579 -0.821297264532518
94 OC301604 9.5009 6764 150.549333333333 115 147.836555181346 120 141.048433333333 138.335655181346 -2.71277815198775
95 00998314 18.9966 1677 159.077 103 160 102 140.0804 141.0034 0.922999999999945
96 THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064 38.4924 381 178.171555555556 81 177.436350655372 82 139.679155555556 138.943950655372 -0.73520490018322
97 03942129 7 12849 146.559666666667 119 148.500250109757 118 139.559666666667 141.500250109757 1.94058344308993
98 04369054 2 211643 141.481333333333 129 143.298790128817 125 139.481333333333 141.298790128817 1.81745679548422
99 ALISTAIR$NA$STEELE$1953$11 6 20851 144.591888888889 121 146 121 138.591888888889 140 1.40811111111108
100 SEGRO PLC$ENGLAND AND WALES$167591 3.4979 65636 139.189555555556 133 140.16761135978 133 135.691655555556 136.66971135978 0.978055804224397
101 OC319972 5.8467 21435 140.911888888889 130 142.333333333333 128 135.065188888889 136.486633333333 1.42144444444446

101
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participant_id,sumdpi,rankdpi,sumnpi,ranknpi,sumtransitive,ranktransitive,diff_npi_dpi,diff_transitive_dpi,diff_transitive_npi
SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624,4,42441,1452.95022222222,1,1482.18842011308,1,1448.95022222222,1478.18842011308,29.2381978908597
ANDREW$SIMON$DAVIS$1963$7,14.5042,2788,869.487555555556,6,881.3365356159,5,854.983355555556,866.8323356159,11.8489800603431
SC095000,5,24872,670.525666666667,8,735.610780469834,7,665.525666666667,730.610780469834,65.0851138031673
11443992,11,5149,591.460888888889,10,669.338549583877,9,580.460888888889,658.338549583877,77.8776606949871
READE$NA$GRIFFITH$1965$4,1.4972,491331,636.465111111111,9,657.49955601355,10,634.967911111111,656.00235601355,21.0344449024385
PERSIMMON PLC$ENGLAND$1818486,14,2911,578.420555555556,11,586.035982151633,11,564.420555555556,572.035982151633,7.6154265960771
INTERTRUST N.V.$THE NETHERLANDS$N/A,1,887094,511.782222222222,12,519.652355682228,12,510.782222222222,518.652355682228,7.87013346000617
08885072,1,1226949,389.079222222222,19,468.031302647188,18,388.079222222222,467.031302647188,78.9520804249655
06035106,14,2982,474.829444444445,16,480.114910906034,15,460.829444444445,466.114910906034,5.28546646158912
10657226,10,6219,342.955333333334,23,462.050947342302,19,332.955333333334,452.050947342302,119.095614008968
00604574,31,587,473.602,17,481.125633609192,14,442.602,450.125633609192,7.5236336091923
11444019,6,17408,386.593444444445,20,403.985152490125,21,380.593444444445,397.985152490125,17.3917080456807
03981143,19,1624,411.697111111111,18,414.491202616254,20,392.697111111111,395.491202616254,2.79409150514357
10510800,1,1535931,366.270333333333,21,370,23,365.270333333333,369,3.72966666666673
SUN LIFE FINANCIAL INC.$CANADA$F380,1,2086664,358.225444444444,22,364.651221643269,24,357.225444444444,363.651221643269,6.42577719882496
00102498,18,1757,336.391666666667,26,377.785641323169,22,318.391666666667,359.785641323169,41.3939746565019
04569346,4,45566,328.479,27,332.883401968393,28,324.479,328.883401968393,4.40440196839307
01417162,13,3477,320.993555555555,28,333.114660129009,27,307.993555555555,320.114660129009,12.121104573454
02468686,3.9928,58547,305.836888888889,29,316.091281388984,29,301.844088888889,312.098481388984,10.2543925000952
03777037,35.4911,458,338.669111111111,25,345.770230509207,25,303.178011111111,310.279130509207,7.10111939809553
00621920,7.5086,11060,295.787333333333,30,301.826105187632,30,288.278733333333,294.317505187632,6.03877185429838
00296805,9.5097,6642,283.340333333333,33,289.902171627357,32,273.830633333333,280.392471627357,6.56183829402386
01142830,17.3204,1948,276.395222222222,35,290.62995167509,31,259.074822222222,273.30955167509,14.2347294528681
02877315,2,176901,269.693888888889,37,273.241267886102,37,267.693888888889,271.241267886102,3.54737899721323
WOODLEY$LARKIN$HUNT$1945$11,1,1331918,256.523555555556,39,261.339361555954,38,255.523555555556,260.339361555954,4.81580600039837
HANNOVER RUCK SE$GERMANY$HRB 6778,3,82217,258.389888888889,38,261,39,255.389888888889,258,2.61011111111122
00082548,39,365,286.73,31,289.415186936244,33,247.73,250.415186936244,2.68518693624372
08340090,1,785896,245.526666666667,43,248,42,244.526666666667,247,2.47333333333344
10763268,2,306820,245.016666666667,44,247.665776742879,44,243.016666666667,245.665776742879,2.6491100762122
04967001,3.1677,71002,242.283111111111,46,247.855191284282,43,239.115411111111,244.687491284282,5.57208017317043
HEIDELBERGCEMENT AG$GERMANY$HRB 33082,2,210440,236.095777777778,48,246.443097797991,45,234.095777777778,244.443097797991,10.3473200202133
OC360196,2,242598,252.407222222222,40,241.635711925833,48,250.407222222222,239.635711925833,-10.7715102963891
08286875,45.8382,268,271.165444444445,36,284.837428399735,35,225.327244444445,238.999228399736,13.6719839552909
CRH PLC$IRELAND$12965,1,617583,230.075888888889,50,235.350874688043,51,229.075888888889,234.350874688043,5.27498579915408
OC332179,2,183094,227.677555555556,52,230.332888592395,52,225.677555555556,228.332888592395,2.65533303683935
SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA,1,961566,229.452111111111,51,229.246004751229,54,228.452111111111,228.246004751229,-0.206106359882426
STEPHEN$STUART SOLOMON$CONWAY$1948$2,10,5851,233.584888888889,49,237.537965323381,50,223.584888888889,227.537965323381,3.95307643449249
OC301825,17,2009,239.057666666667,47,242.212988425641,47,222.057666666667,225.212988425641,3.15532175897408
BRYAN$ANTHONY$THORNTON$1955$7,69.9992,135,284.260888888889,32,287.332221480987,34,214.261688888889,217.333021480987,3.07133259209854
01470151,38,387,251.364888888889,42,252.900520102143,40,213.364888888889,214.900520102143,1.53563121325368
MICHAEL$BARRY$TABOR$1941$10,2,194884,211.140666666667,60,214.829760965527,58,209.140666666667,212.829760965527,3.68909429886025
00306718,2,173704,211.167444444445,59,213.813343161875,59,209.167444444445,211.813343161875,2.64589871743056
SC045551,4,42589,211.497,58,213.557523551435,60,207.497,209.557523551435,2.06052355143524
BELLWAY P.L.C.$ENGLAND$1372603,21,1279,227.340222222222,53,229.460570633214,53,206.340222222222,208.460570633214,2.12034841099197
05172586,1,619407,207.170222222222,64,209.167889557863,63,206.170222222222,208.167889557863,1.99766733564073
RADOVAN$NA$KOLJEVIC$1967$5,4,47760,208.412777777778,63,210.999332888592,62,204.412777777778,206.999332888592,2.58655511081454
03140521,35.5041,453,226.638222222222,55,241.120645742615,49,191.134122222222,205.616545742615,14.4824235203928
06397765,7.5069,11088,208.652111111111,62,211.130367917775,61,201.145211111111,203.623467917775,2.47825680666418
OLUWOLE$NA$KOLADE$1966$11,4,57071,197.168333333333,70,204.402107259893,66,193.168333333333,200.402107259893,7.23377392655939
BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4,19.5484,1526,216.430333333333,56,215.557869788565,57,196.881933333333,196.009469788565,-0.872463544768436
ROMY$ELIZABETH$SUMMERSKILL$1967$1,6.5042,15243,199.066222222222,68,200.878082442063,69,192.562022222222,194.373882442063,1.81186021984072
SENTTHURAN$NA$NADARAJAH$1979$11,13,3685,205.072666666667,66,207,64,192.072666666667,194,1.92733333333339
00521970,24,969,209.580444444445,61,217.943276147564,56,185.580444444444,193.943276147564,8.3628317031195
04120344,1,592751,191.048666666667,71,193.500249906766,72,190.048666666667,192.500249906766,2.45158324009947
KEITH$NA$BRESLAUER$1966$3,3.0098,71852,190.085222222222,72,192.94594185951,73,187.075422222222,189.93614185951,2.86071963728801
OC313101,10.0091,5699,189.673777777778,73,191.798555400488,74,179.664677777778,181.789455400488,2.12477762271021
PATRICK$ANTHONY$MCKENNA$1956$6,7,13432,182.905444444444,79,184.950746253802,75,175.905444444444,177.950746253802,2.04530180935731
MANJIT$NA$DALE$1965$6,2.3176,162072,163.911666666667,92,178.248028826349,81,161.594066666667,175.930428826349,14.3363621596826
STEPHEN$JAMES$ROBERTSON$1960$3,2.3488,156655,186.561666666667,76,178.248028826349,80,184.212866666667,175.899228826349,-8.31363784031754
SC286832,19,1623,189.588777777778,74,194.009419943477,71,170.588777777778,175.009419943477,4.42064216569923
JEAN-GUY$NA$DESJARDINS$1944$10,8,9585,165.875,88,180.731962006548,78,157.875,172.731962006548,14.8569620065477
04330127,2,185351,172.353,85,174.666277436318,85,170.353,172.666277436318,2.31327743631806
GUY$NA$HANDS$1959$8,12.5038,3793,183.917666666667,77,183.377417210637,76,171.413866666667,170.873617210637,-0.540249456029898
VISTRY (JERSEY) LIMITED$JERSEY$130175,1,672013,161.530777777778,99,171.767151202623,87,160.530777777778,170.767151202623,10.2363734248455
QATAR INVESTMENT AUTHORITY$QATAR$/,0.9864,2818663,150.943333333333,114,170.469159583876,91,149.956933333333,169.482759583876,19.5258262505427
BROOKFIELD ASSET MANAGEMENT INC$CANADA$/,1.0136,555776,186.598,75,170.469159583876,90,185.5844,169.455559583876,-16.1288404161239
06394563,3,78751,168.266,86,170.02573434901,92,165.266,167.02573434901,1.75973434901024
07023200,1,962994,165.817333333333,89,167.665219974605,95,164.817333333333,166.665219974605,1.84788664127171
OC333409,4,42092,164.090222222222,91,169.773887544448,93,160.090222222222,165.773887544448,5.68366532222564
SOFTBANK GROUP CORP$JAPAN$0104-01-056795,3,80640,163.836444444444,93,168.66025626587,94,160.836444444444,165.66025626587,4.82381182142512
11499533,1,1443396,162.169888888889,97,163.898038919407,97,161.169888888889,162.898038919407,1.72815003051784
07934492,8,9563,168.187111111111,87,170.819869720549,88,160.187111111111,162.819869720549,2.63275860943807
08379990,11.4977,4578,162.343222222222,96,172.558543709203,86,150.845522222222,161.060843709203,10.2153214869812
00445790,19.5101,1527,178.167555555556,82,180.399232361494,79,158.657455555556,160.889132361494,2.23167680593886
03199160,4,42466,162.718555555556,94,164.33318506947,96,158.718555555556,160.33318506947,1.61462951391485
02708030,2,179758,160.509555555556,101,161.051230246867,101,158.509555555556,159.051230246867,0.54167469131167
11606773,3,93217,162.071444444444,98,161.809404862073,99,159.071444444444,158.809404862073,-0.262039582371528
SEAN$MICHAEL$DINNEN$1968$3,1,2659434,157.004444444444,106,158.573288802633,103,156.004444444444,157.573288802633,1.56884435818873
CASTLE BIDCO LIMITED$UNITED KINGDOM$5988526,1,609460,157.867666666667,105,158.345681428497,104,156.867666666667,157.345681428497,0.478014761829996
00617987,15.2227,2511,160.153666666667,102,170.760746414119,89,144.930966666667,155.538046414119,10.6070797474518
THE BRITISH UNITED PROVIDENT ASSOCIATION LIMITED$ENGLAND$432511,1,656307,154.393222222222,108,155.868768815271,106,153.393222222222,154.868768815271,1.47554659304876
STEPHEN$ALLEN$SCHWARZMAN$1947$2,90,96,243.444333333333,45,244.6992587951,46,153.444333333333,154.6992587951,1.25492546176619
IMRAN$NA$HAKIM$1977$9,4.6661,33921,154.101666666667,110,158.30270905129,105,149.435566666667,153.63660905129,4.20104238462346
CHARLES$GUY$CAMROUX-OLIVER$1970$4,1.2452,551192,162.649666666667,95,151.791367871721,110,161.404466666667,150.546167871721,-10.8582987949457
TIMOTHY$PATRICK CAMROUX$OLIVER$1944$3,0.2488,3911463,183.432777777778,78,150.791367871721,113,183.183977777778,150.542567871721,-32.6414099060569
JAMES$RICHARD$CAMROUX-OLIVER$1967$9,0.2506,3909000,129.433666666667,144,150.791367871721,111,129.183066666667,150.540767871721,21.3577012050542
ALEXA$KATE LOUISE CAMROUX$PEARMUND$1974$12,0.2554,3903961,122.389,164,150.791367871721,112,122.1336,150.535967871721,28.402367871721
00293262,1,594882,148.146333333333,117,150.022282279097,114,147.146333333333,149.022282279097,1.87594894576387
THE LEADERS ROMANS MIDCO2 LIMITED$ENGLAND$9939213,1,1399100,147.481333333333,118,149,116,146.481333333333,148,1.51866666666672
OC329299,7,13415,157.924333333333,104,153.688376714201,109,150.924333333333,146.688376714201,-4.23595661913217
08669482,6.507,15133,149.444111111111,116,148.622813846579,117,142.937111111111,142.115813846579,-0.821297264532518
03942129,7,12849,146.559666666667,119,148.500250109757,118,139.559666666667,141.500250109757,1.94058344308993
04369054,2,211643,141.481333333333,129,143.298790128817,125,139.481333333333,141.298790128817,1.81745679548422
00998314,18.9966,1677,159.077,103,160,102,140.0804,141.0034,0.922999999999945
MARK$DAVID$STOTT$1972$4,8,9812,151.257777777778,113,148.326943547396,119,143.257777777778,140.326943547396,-2.93083423038166
ALISTAIR$NA$STEELE$1953$11,6,20851,144.591888888889,121,146,121,138.591888888889,140,1.40811111111108
GRANDVISION N.V.$NETHERLANDS$50338269,2,226915,135.064333333333,141,141.853357055101,131,133.064333333333,139.853357055101,6.78902372176793
SONY CORPORATION$JAPAN$5010401067252,10,5898,143.083555555556,126,149.025068804305,115,133.083555555556,139.025068804305,5.94151324874986
THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064,38.4924,381,178.171555555556,81,177.436350655372,82,139.679155555556,138.943950655372,-0.73520490018322
OC301604,9.5009,6764,150.549333333333,115,147.836555181346,120,141.048433333333,138.335655181346,-2.71277815198775
1 participant_id sumdpi rankdpi sumnpi ranknpi sumtransitive ranktransitive diff_npi_dpi diff_transitive_dpi diff_transitive_npi
2 SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624 4 42441 1452.95022222222 1 1482.18842011308 1 1448.95022222222 1478.18842011308 29.2381978908597
3 ANDREW$SIMON$DAVIS$1963$7 14.5042 2788 869.487555555556 6 881.3365356159 5 854.983355555556 866.8323356159 11.8489800603431
4 SC095000 5 24872 670.525666666667 8 735.610780469834 7 665.525666666667 730.610780469834 65.0851138031673
5 11443992 11 5149 591.460888888889 10 669.338549583877 9 580.460888888889 658.338549583877 77.8776606949871
6 READE$NA$GRIFFITH$1965$4 1.4972 491331 636.465111111111 9 657.49955601355 10 634.967911111111 656.00235601355 21.0344449024385
7 PERSIMMON PLC$ENGLAND$1818486 14 2911 578.420555555556 11 586.035982151633 11 564.420555555556 572.035982151633 7.6154265960771
8 INTERTRUST N.V.$THE NETHERLANDS$N/A 1 887094 511.782222222222 12 519.652355682228 12 510.782222222222 518.652355682228 7.87013346000617
9 08885072 1 1226949 389.079222222222 19 468.031302647188 18 388.079222222222 467.031302647188 78.9520804249655
10 06035106 14 2982 474.829444444445 16 480.114910906034 15 460.829444444445 466.114910906034 5.28546646158912
11 10657226 10 6219 342.955333333334 23 462.050947342302 19 332.955333333334 452.050947342302 119.095614008968
12 00604574 31 587 473.602 17 481.125633609192 14 442.602 450.125633609192 7.5236336091923
13 11444019 6 17408 386.593444444445 20 403.985152490125 21 380.593444444445 397.985152490125 17.3917080456807
14 03981143 19 1624 411.697111111111 18 414.491202616254 20 392.697111111111 395.491202616254 2.79409150514357
15 10510800 1 1535931 366.270333333333 21 370 23 365.270333333333 369 3.72966666666673
16 SUN LIFE FINANCIAL INC.$CANADA$F380 1 2086664 358.225444444444 22 364.651221643269 24 357.225444444444 363.651221643269 6.42577719882496
17 00102498 18 1757 336.391666666667 26 377.785641323169 22 318.391666666667 359.785641323169 41.3939746565019
18 04569346 4 45566 328.479 27 332.883401968393 28 324.479 328.883401968393 4.40440196839307
19 01417162 13 3477 320.993555555555 28 333.114660129009 27 307.993555555555 320.114660129009 12.121104573454
20 02468686 3.9928 58547 305.836888888889 29 316.091281388984 29 301.844088888889 312.098481388984 10.2543925000952
21 03777037 35.4911 458 338.669111111111 25 345.770230509207 25 303.178011111111 310.279130509207 7.10111939809553
22 00621920 7.5086 11060 295.787333333333 30 301.826105187632 30 288.278733333333 294.317505187632 6.03877185429838
23 00296805 9.5097 6642 283.340333333333 33 289.902171627357 32 273.830633333333 280.392471627357 6.56183829402386
24 01142830 17.3204 1948 276.395222222222 35 290.62995167509 31 259.074822222222 273.30955167509 14.2347294528681
25 02877315 2 176901 269.693888888889 37 273.241267886102 37 267.693888888889 271.241267886102 3.54737899721323
26 WOODLEY$LARKIN$HUNT$1945$11 1 1331918 256.523555555556 39 261.339361555954 38 255.523555555556 260.339361555954 4.81580600039837
27 HANNOVER RUCK SE$GERMANY$HRB 6778 3 82217 258.389888888889 38 261 39 255.389888888889 258 2.61011111111122
28 00082548 39 365 286.73 31 289.415186936244 33 247.73 250.415186936244 2.68518693624372
29 08340090 1 785896 245.526666666667 43 248 42 244.526666666667 247 2.47333333333344
30 10763268 2 306820 245.016666666667 44 247.665776742879 44 243.016666666667 245.665776742879 2.6491100762122
31 04967001 3.1677 71002 242.283111111111 46 247.855191284282 43 239.115411111111 244.687491284282 5.57208017317043
32 HEIDELBERGCEMENT AG$GERMANY$HRB 33082 2 210440 236.095777777778 48 246.443097797991 45 234.095777777778 244.443097797991 10.3473200202133
33 OC360196 2 242598 252.407222222222 40 241.635711925833 48 250.407222222222 239.635711925833 -10.7715102963891
34 08286875 45.8382 268 271.165444444445 36 284.837428399735 35 225.327244444445 238.999228399736 13.6719839552909
35 CRH PLC$IRELAND$12965 1 617583 230.075888888889 50 235.350874688043 51 229.075888888889 234.350874688043 5.27498579915408
36 OC332179 2 183094 227.677555555556 52 230.332888592395 52 225.677555555556 228.332888592395 2.65533303683935
37 SEMPERIAN PPP INVESTMENT PARTNERS HOLDINGS LIMITED$NA$NA 1 961566 229.452111111111 51 229.246004751229 54 228.452111111111 228.246004751229 -0.206106359882426
38 STEPHEN$STUART SOLOMON$CONWAY$1948$2 10 5851 233.584888888889 49 237.537965323381 50 223.584888888889 227.537965323381 3.95307643449249
39 OC301825 17 2009 239.057666666667 47 242.212988425641 47 222.057666666667 225.212988425641 3.15532175897408
40 BRYAN$ANTHONY$THORNTON$1955$7 69.9992 135 284.260888888889 32 287.332221480987 34 214.261688888889 217.333021480987 3.07133259209854
41 01470151 38 387 251.364888888889 42 252.900520102143 40 213.364888888889 214.900520102143 1.53563121325368
42 MICHAEL$BARRY$TABOR$1941$10 2 194884 211.140666666667 60 214.829760965527 58 209.140666666667 212.829760965527 3.68909429886025
43 00306718 2 173704 211.167444444445 59 213.813343161875 59 209.167444444445 211.813343161875 2.64589871743056
44 SC045551 4 42589 211.497 58 213.557523551435 60 207.497 209.557523551435 2.06052355143524
45 BELLWAY P.L.C.$ENGLAND$1372603 21 1279 227.340222222222 53 229.460570633214 53 206.340222222222 208.460570633214 2.12034841099197
46 05172586 1 619407 207.170222222222 64 209.167889557863 63 206.170222222222 208.167889557863 1.99766733564073
47 RADOVAN$NA$KOLJEVIC$1967$5 4 47760 208.412777777778 63 210.999332888592 62 204.412777777778 206.999332888592 2.58655511081454
48 03140521 35.5041 453 226.638222222222 55 241.120645742615 49 191.134122222222 205.616545742615 14.4824235203928
49 06397765 7.5069 11088 208.652111111111 62 211.130367917775 61 201.145211111111 203.623467917775 2.47825680666418
50 OLUWOLE$NA$KOLADE$1966$11 4 57071 197.168333333333 70 204.402107259893 66 193.168333333333 200.402107259893 7.23377392655939
51 BENZION$SCHALOM ELIEZER$FRESHWATER$1948$4 19.5484 1526 216.430333333333 56 215.557869788565 57 196.881933333333 196.009469788565 -0.872463544768436
52 ROMY$ELIZABETH$SUMMERSKILL$1967$1 6.5042 15243 199.066222222222 68 200.878082442063 69 192.562022222222 194.373882442063 1.81186021984072
53 SENTTHURAN$NA$NADARAJAH$1979$11 13 3685 205.072666666667 66 207 64 192.072666666667 194 1.92733333333339
54 00521970 24 969 209.580444444445 61 217.943276147564 56 185.580444444444 193.943276147564 8.3628317031195
55 04120344 1 592751 191.048666666667 71 193.500249906766 72 190.048666666667 192.500249906766 2.45158324009947
56 KEITH$NA$BRESLAUER$1966$3 3.0098 71852 190.085222222222 72 192.94594185951 73 187.075422222222 189.93614185951 2.86071963728801
57 OC313101 10.0091 5699 189.673777777778 73 191.798555400488 74 179.664677777778 181.789455400488 2.12477762271021
58 PATRICK$ANTHONY$MCKENNA$1956$6 7 13432 182.905444444444 79 184.950746253802 75 175.905444444444 177.950746253802 2.04530180935731
59 MANJIT$NA$DALE$1965$6 2.3176 162072 163.911666666667 92 178.248028826349 81 161.594066666667 175.930428826349 14.3363621596826
60 STEPHEN$JAMES$ROBERTSON$1960$3 2.3488 156655 186.561666666667 76 178.248028826349 80 184.212866666667 175.899228826349 -8.31363784031754
61 SC286832 19 1623 189.588777777778 74 194.009419943477 71 170.588777777778 175.009419943477 4.42064216569923
62 JEAN-GUY$NA$DESJARDINS$1944$10 8 9585 165.875 88 180.731962006548 78 157.875 172.731962006548 14.8569620065477
63 04330127 2 185351 172.353 85 174.666277436318 85 170.353 172.666277436318 2.31327743631806
64 GUY$NA$HANDS$1959$8 12.5038 3793 183.917666666667 77 183.377417210637 76 171.413866666667 170.873617210637 -0.540249456029898
65 VISTRY (JERSEY) LIMITED$JERSEY$130175 1 672013 161.530777777778 99 171.767151202623 87 160.530777777778 170.767151202623 10.2363734248455
66 QATAR INVESTMENT AUTHORITY$QATAR$/ 0.9864 2818663 150.943333333333 114 170.469159583876 91 149.956933333333 169.482759583876 19.5258262505427
67 BROOKFIELD ASSET MANAGEMENT INC$CANADA$/ 1.0136 555776 186.598 75 170.469159583876 90 185.5844 169.455559583876 -16.1288404161239
68 06394563 3 78751 168.266 86 170.02573434901 92 165.266 167.02573434901 1.75973434901024
69 07023200 1 962994 165.817333333333 89 167.665219974605 95 164.817333333333 166.665219974605 1.84788664127171
70 OC333409 4 42092 164.090222222222 91 169.773887544448 93 160.090222222222 165.773887544448 5.68366532222564
71 SOFTBANK GROUP CORP$JAPAN$0104-01-056795 3 80640 163.836444444444 93 168.66025626587 94 160.836444444444 165.66025626587 4.82381182142512
72 11499533 1 1443396 162.169888888889 97 163.898038919407 97 161.169888888889 162.898038919407 1.72815003051784
73 07934492 8 9563 168.187111111111 87 170.819869720549 88 160.187111111111 162.819869720549 2.63275860943807
74 08379990 11.4977 4578 162.343222222222 96 172.558543709203 86 150.845522222222 161.060843709203 10.2153214869812
75 00445790 19.5101 1527 178.167555555556 82 180.399232361494 79 158.657455555556 160.889132361494 2.23167680593886
76 03199160 4 42466 162.718555555556 94 164.33318506947 96 158.718555555556 160.33318506947 1.61462951391485
77 02708030 2 179758 160.509555555556 101 161.051230246867 101 158.509555555556 159.051230246867 0.54167469131167
78 11606773 3 93217 162.071444444444 98 161.809404862073 99 159.071444444444 158.809404862073 -0.262039582371528
79 SEAN$MICHAEL$DINNEN$1968$3 1 2659434 157.004444444444 106 158.573288802633 103 156.004444444444 157.573288802633 1.56884435818873
80 CASTLE BIDCO LIMITED$UNITED KINGDOM$5988526 1 609460 157.867666666667 105 158.345681428497 104 156.867666666667 157.345681428497 0.478014761829996
81 00617987 15.2227 2511 160.153666666667 102 170.760746414119 89 144.930966666667 155.538046414119 10.6070797474518
82 THE BRITISH UNITED PROVIDENT ASSOCIATION LIMITED$ENGLAND$432511 1 656307 154.393222222222 108 155.868768815271 106 153.393222222222 154.868768815271 1.47554659304876
83 STEPHEN$ALLEN$SCHWARZMAN$1947$2 90 96 243.444333333333 45 244.6992587951 46 153.444333333333 154.6992587951 1.25492546176619
84 IMRAN$NA$HAKIM$1977$9 4.6661 33921 154.101666666667 110 158.30270905129 105 149.435566666667 153.63660905129 4.20104238462346
85 CHARLES$GUY$CAMROUX-OLIVER$1970$4 1.2452 551192 162.649666666667 95 151.791367871721 110 161.404466666667 150.546167871721 -10.8582987949457
86 TIMOTHY$PATRICK CAMROUX$OLIVER$1944$3 0.2488 3911463 183.432777777778 78 150.791367871721 113 183.183977777778 150.542567871721 -32.6414099060569
87 JAMES$RICHARD$CAMROUX-OLIVER$1967$9 0.2506 3909000 129.433666666667 144 150.791367871721 111 129.183066666667 150.540767871721 21.3577012050542
88 ALEXA$KATE LOUISE CAMROUX$PEARMUND$1974$12 0.2554 3903961 122.389 164 150.791367871721 112 122.1336 150.535967871721 28.402367871721
89 00293262 1 594882 148.146333333333 117 150.022282279097 114 147.146333333333 149.022282279097 1.87594894576387
90 THE LEADERS ROMANS MIDCO2 LIMITED$ENGLAND$9939213 1 1399100 147.481333333333 118 149 116 146.481333333333 148 1.51866666666672
91 OC329299 7 13415 157.924333333333 104 153.688376714201 109 150.924333333333 146.688376714201 -4.23595661913217
92 08669482 6.507 15133 149.444111111111 116 148.622813846579 117 142.937111111111 142.115813846579 -0.821297264532518
93 03942129 7 12849 146.559666666667 119 148.500250109757 118 139.559666666667 141.500250109757 1.94058344308993
94 04369054 2 211643 141.481333333333 129 143.298790128817 125 139.481333333333 141.298790128817 1.81745679548422
95 00998314 18.9966 1677 159.077 103 160 102 140.0804 141.0034 0.922999999999945
96 MARK$DAVID$STOTT$1972$4 8 9812 151.257777777778 113 148.326943547396 119 143.257777777778 140.326943547396 -2.93083423038166
97 ALISTAIR$NA$STEELE$1953$11 6 20851 144.591888888889 121 146 121 138.591888888889 140 1.40811111111108
98 GRANDVISION N.V.$NETHERLANDS$50338269 2 226915 135.064333333333 141 141.853357055101 131 133.064333333333 139.853357055101 6.78902372176793
99 SONY CORPORATION$JAPAN$5010401067252 10 5898 143.083555555556 126 149.025068804305 115 133.083555555556 139.025068804305 5.94151324874986
100 THE BERKELEY GROUP PLC$ENGLAND & WALES$1454064 38.4924 381 178.171555555556 81 177.436350655372 82 139.679155555556 138.943950655372 -0.73520490018322
101 OC301604 9.5009 6764 150.549333333333 115 147.836555181346 120 141.048433333333 138.335655181346 -2.71277815198775

101
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participant_id,sumdpi,rankdpi,sumnpi,ranknpi,sumtransitive,ranktransitive,diff_npi_dpi,diff_transitive_dpi,diff_transitive_npi
10657226,10,6219,342.955333333334,23,462.050947342302,19,332.955333333334,452.050947342302,119.095614008968
08885072,1,1226949,389.079222222222,19,468.031302647188,18,388.079222222222,467.031302647188,78.9520804249655
11443992,11,5149,591.460888888889,10,669.338549583877,9,580.460888888889,658.338549583877,77.8776606949871
SC095000,5,24872,670.525666666667,8,735.610780469834,7,665.525666666667,730.610780469834,65.0851138031673
03954113,0,3928492,0,3928492,56.3302557872759,564,0,56.3302557872759,56.3302557872759
00102498,18,1757,336.391666666667,26,377.785641323169,22,318.391666666667,359.785641323169,41.3939746565019
04220587,0,3938440,0,3938440,40.9288958121612,898,0,40.9288958121612,40.9288958121612
SURINDER$SINGH$TOOR$1972$3,2.5015,140665,39.3167777777778,947,73.9610142643602,357,36.8152777777778,71.4595142643602,34.6442364865824
02622406,1,953107,38.5817777777778,985,70.2113074441665,391,37.5817777777778,69.2113074441665,31.6295296663887
GARY$WILLIAM$TIPPER$1963$7,1.3341,536858,99.1909999999999,223,129.988376131723,146,97.8569,128.654276131723,30.7973761317235
SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624,4,42441,1452.95022222222,1,1482.18842011308,1,1448.95022222222,1478.18842011308,29.2381978908597
RICHARD$LEONARD$SIMMONDS$1979$12,6.5138,15035,6.48166666666667,20445,35.4645679773307,1114,-0.0321333333333325,28.9507679773307,28.9829013106641
RUPERT$CHARLES GIFFORD$LYWOOD$1958$5,7.9889,10834,47.7837777777778,702,76.5569512712771,338,39.7948777777778,68.568051271277,28.7731734934993
ALEXA$KATE LOUISE CAMROUX$PEARMUND$1974$12,0.2554,3903961,122.389,164,150.791367871721,112,122.1336,150.535967871721,28.402367871721
MARK$NA$JOSPEH$1968$4,0,4034257,0,4034257,25.1249995937727,1853,0,25.1249995937727,25.1249995937727
HEINZ$HEINRICH$BAUER$1939$10,0,3971319,0,3971319,24.4692916321143,1966,0,24.4692916321143,24.4692916321143
BAJLINDER$KAUR$BOPARAN$1968$1,0,3961511,0,3961511,24.3750001727124,1972,0,24.3750001727124,24.3750001727124
OC326165,6,17447,103.840111111111,209,127.677935557153,150,97.8401111111111,121.677935557153,23.8378244460417
MATTHEW$JAMES$WOODS$1975$12,3.8241,59659,36.409,1084,58.7450903400284,538,32.5849,54.9209903400284,22.3360903400283
JAMES$RICHARD$CAMROUX-OLIVER$1967$9,0.2506,3909000,129.433666666667,144,150.791367871721,111,129.183066666667,150.540767871721,21.3577012050542
READE$NA$GRIFFITH$1965$4,1.4972,491331,636.465111111111,9,657.49955601355,10,634.967911111111,656.00235601355,21.0344449024385
JOHN$NA$MCDONAGH$1969$5,1,1427664,87.3861111111112,276,107.213226733802,198,86.3861111111112,106.213226733802,19.8271156226908
QATAR INVESTMENT AUTHORITY$QATAR$/,0.9864,2818663,150.943333333333,114,170.469159583876,91,149.956933333333,169.482759583876,19.5258262505427
MICHELE$CAROLINE$GIDDENS$1965$9,0.9972,2793601,64.0042222222222,457,82.8732036087854,304,63.0070222222222,81.8760036087855,18.8689813865632
MINISTRY OF FINANCE$NA$NA,1,876006,1,846460,19.8318760999104,2774,0,18.8318760999104,18.8318760999104
SAMUEL$GEORGE ARMSTRONG$VESTEY$1941$3,1,593454,1,604909,19.1250009915149,2878,0,18.1250009915149,18.1250009915149
LAURENCE$JON$FUMAGALLI$1972$4,0.3379,3785704,37.7572222222222,1026,55.6425456988741,572,37.4193222222222,55.3046456988741,17.8853234766518
TAREQ$NA$NAQIB$1971$12,0,3948415,0,3948415,17.6250004758762,3357,0,17.6250004758762,17.6250004758762
11444019,6,17408,386.593444444445,20,403.985152490125,21,380.593444444445,397.985152490125,17.3917080456807
JENNIFER$CHRISTINE$LANCE$1966$9,0,3935050,0,3935050,16.7499169617751,3669,0,16.7499169617751,16.7499169617751
MICHAEL$JOSEPH$RYAN$1966$4,1,1431899,91.9212222222223,255,107.213226725418,199,90.9212222222223,106.213226725418,15.2920045031962
RONAN$NA$KILDUFF$1977$11,2,258052,40.3115555555556,909,55.5248600177933,575,38.3115555555556,53.5248600177933,15.2133044622377
JEAN-GUY$NA$DESJARDINS$1944$10,8,9585,165.875,88,180.731962006548,78,157.875,172.731962006548,14.8569620065477
03140521,35.5041,453,226.638222222222,55,241.120645742615,49,191.134122222222,205.616545742615,14.4824235203928
MANJIT$NA$DALE$1965$6,2.3176,162072,163.911666666667,92,178.248028826349,81,161.594066666667,175.930428826349,14.3363621596826
FREDERICK$PAUL$GRAHAM-WATSON$1957$9,0.6741,2838997,0.337333333333333,3651011,14.583333305857,4612,-0.336766666666667,13.909233305857,14.2459999725236
01142830,17.3204,1948,276.395222222222,35,290.62995167509,31,259.074822222222,273.30955167509,14.2347294528681
09405653,2.3244,161817,11.1937777777778,7225,25.270673368002,1841,8.86937777777778,22.946273368002,14.0768955902242
08286875,45.8382,268,271.165444444445,36,284.837428399735,35,225.327244444445,238.999228399736,13.6719839552909
LORRAINE$GERALDINE$SPENCER$1959$5,0.4936,3669613,0.491888888888889,3568226,14.1200884354501,4801,-0.001711111111111,13.6264884354501,13.6281995465612
DAVID$JEREMY$COURTENAY-STAMP$1962$4,0.4911,3727778,0.495222222222222,3462306,14.1200884354501,4800,0.00412222222222203,13.6289884354501,13.6248662132279
00395826,8,9152,107.014666666667,196,120.608813410091,167,99.0146666666666,112.608813410091,13.5941467434246
LEON$PAUL$JONES$1980$4,4.9752,33464,4.993,36314,18.564442877988,3069,0.0177999999999994,13.589242877988,13.571442877988
INFLEXION PARTNERSHIP CAPITAL FUND I GENERAL PARTNER GUERNSEY LIMITED (AS GP OF INFLEXION PARTNERSHIP CAPITAL FUND I GENERAL PARTNER GUERNSEY LP)$GUERNSEY$2075,0,4017857,0,4017857,13.4999998990969,5310,0,13.4999998990969,13.4999998990969
WILLIAM$BRUCE$KENDALL$1961$8,3.3652,68795,25.8097777777778,1799,39.2585890720939,949,22.4445777777778,35.8933890720939,13.4488112943161
EMILIO$NA$DI SPIEZIO SARDO$1977$3,0.4986,3404264,0.502333333333333,3035959,13.9507883608242,5119,0.00373333333333298,13.4521883608242,13.4484550274908
TRISTAN$NICHOLAS$RAMUS$1972$9,1.5078,415660,10.7518888888889,8051,24,1998,9.24408888888889,22.4922,13.2481111111111
STEPHEN$BERNARD$LILLEY$1968$4,0.3332,3834029,42.5912222222222,840,55.6425456988741,573,42.2580222222222,55.3093456988741,13.0513234766518
PETER$STEVEN CHRISTOPHER$BRODNICKI$1962$5,2,200423,40.178,913,53.145803755235,604,38.178,51.145803755235,12.967803755235
12242839,0,3952163,0,3952163,12.950317378398,5822,0,12.950317378398,12.950317378398
"LO HOLDING SA$GENEVA, SWITZERLAND$CH-660.1.793.002-5",1,971706,19.2664444444445,2881,31.9039719623088,1325,18.2664444444445,30.9039719623088,12.6375275178643
ETL INTERNATIONAL AG$GERMANY$DE281293152,1,1101695,34.641,1163,47.1368207299801,720,33.641,46.1368207299801,12.4958207299801
ANN$HERON$GLOAG$1942$12,14.8211,2760,48.6741111111111,673,60.894495044748,507,33.8530111111111,46.073395044748,12.2203839336369
01417162,13,3477,320.993555555555,28,333.114660129009,27,307.993555555555,320.114660129009,12.121104573454
BARRY$MICHAEL$LAMBERT$1950$6,0.5063,2939590,0.487777777777778,3613444,12.5000001377942,5977,-0.018522222222222,11.9937001377942,12.0122223600164
"ARES MANAGEMENT, LP$UNITED STATES$5434226",0,3978278,0,3978278,12.0000016961216,6231,0,12.0000016961216,12.0000016961216
ASHLEY$NA$SHAFFER$1998$6,0,3990947,0,3990947,11.8975784234647,6695,0,11.8975784234647,11.8975784234647
ANDREW$SIMON$DAVIS$1963$7,14.5042,2788,869.487555555556,6,881.3365356159,5,854.983355555556,866.8323356159,11.8489800603431
SCULPTOR FINANCE (CO) IRELAND DAC$IRELAND$IE505730,0,4001939,0,4001939,11.6249997005068,6844,0,11.6249997005068,11.6249997005068
SANDRA$JANE$THOMAS$1959$6,0.4972,3497712,0.498111111111111,3306292,11.7499998716466,6765,0.000911111111111029,11.2527998716466,11.2518887605355
JOHN$ANDREW$GATLEY$1964$10,0.5029,3104410,1.48466666666667,527841,12.5623124763371,5969,0.981766666666668,12.0594124763371,11.0776458096704
CORRINA$DAWN$BRYANT$1969$5,0,3933043,0,3933043,10.9503433326613,7818,0,10.9503433326613,10.9503433326613
DANIEL$NA$GRABINER$1989$6,1.6637,405971,1.656,412609,12.5892858526144,5956,-0.00769999999999915,10.9255858526144,10.9332858526144
THOMAS$HENRY GREVILLE$HOWARD$1983$8,0,3935727,0,3935727,10.9146088862447,7829,0,10.9146088862447,10.9146088862447
ANDREW$WILLIAM$JOHNSON$1963$9,3.3326,69890,37.232,1048,47.8429172054689,714,33.8994,44.5103172054689,10.6109172054689
00617987,15.2227,2511,160.153666666667,102,170.760746414119,89,144.930966666667,155.538046414119,10.6070797474518
MICHAEL$DOMINIC WELLS$HALL$1972$3,0.5027,3111819,0.486333333333333,3618157,10.9999998810223,7805,-0.016366666666667,10.4972998810223,10.513666547689
HEIDELBERGCEMENT AG$GERMANY$HRB 33082,2,210440,236.095777777778,48,246.443097797991,45,234.095777777778,244.443097797991,10.3473200202133
MICHAEL$JAMES$BLAKE$1968$2,0.494,3657945,27.7928888888889,1590,38.1248797687994,1002,27.2988888888889,37.6308797687994,10.3319908799105
RICHARD$NICHOLAS ROSTRON$JONES$1966$4,2,303842,3.98344444444444,63402,14.2451502669142,4761,1.98344444444444,12.2451502669142,10.2617058224698
02468686,3.9928,58547,305.836888888889,29,316.091281388984,29,301.844088888889,312.098481388984,10.2543925000952
VISTRY (JERSEY) LIMITED$JERSEY$130175,1,672013,161.530777777778,99,171.767151202623,87,160.530777777778,170.767151202623,10.2363734248455
08379990,11.4977,4578,162.343222222222,96,172.558543709203,86,150.845522222222,161.060843709203,10.2153214869812
HENRY$WILLIAM$MCCOWEN$1971$12,2.8206,129307,2.83877777777778,138598,13.0007567655629,5423,0.0181777777777778,10.1801567655629,10.1619789877851
SAMIT$NA$UNADKAT$1984$12,2.5044,135873,3.36233333333333,78854,13.4999999623873,5309,0.857933333333333,10.9955999623873,10.1376666290539
NAOMI$NA$ACKERMAN$1945$6,1.4977,486950,1.49566666666667,502378,11.625,6837,-0.00203333333333311,10.1273,10.1293333333333
ISSAM$NA$HAMID$1975$10,2,299961,2,292484,12.1249999906485,6199,0,10.1249999906485,10.1249999906485
03633621,2,172902,90.2366666666666,267,100.349439779867,219,88.2366666666666,98.3494397798666,10.1127731132
ZACHARY$NA$BISHTI$1988$7,3,108334,20.333,2634,30.4273895728086,1397,17.333,27.4273895728086,10.0943895728086
01043742,1,625767,14.8533333333333,4592,24.9024019556525,1921,13.8533333333333,23.9024019556525,10.0490686223191
PETER$ALBERT$COOPER$1953$10,4,42113,4,49247,14,5095,0,10,10
SACHIN$NA$UNADKAT$1982$6,15.5009,2459,15.5034444444444,4190,25.4999999623873,1824,0.00254444444444424,9.99909996238727,9.99655551794283
GARRY$NA$WARD$1961$7,2.3325,159728,13.4524444444444,5312,23.3249281555421,2108,11.1199444444444,20.9924281555421,9.87248371109761
GREENCORE HOLDINGS DESIGNATED ACTIVITY COMPANY$IRELAND$189728,0,3963575,0,3963575,9.75000020519733,9402,0,9.75000020519733,9.75000020519733
"INTERNATIONAL CONSOLIDATED AIRLINES GROUP S.A$SPAIN$M-492,129",0,3926334,0,3926334,9.6976830456954,9454,0,9.6976830456954,9.6976830456954
KELLY$PATRICIA$LYNCH$1978$1,0,4014781,0,4014781,9.68490491039554,9458,0,9.68490491039554,9.68490491039554
01571671,0,3926881,0,3926881,9.58333352036852,9574,0,9.58333352036852,9.58333352036852
JOANNA$AVRIL$GREENSLADE$1971$6,3.9861,58877,68.6014444444444,406,78.1836318506682,334,64.6153444444445,74.1975318506682,9.58218740622378
SOCIETE GENERALE SA$FRANCE$522 120 222,1,686548,33.0712222222222,1241,42.4430451234882,853,32.0712222222222,41.4430451234882,9.37182290126601
MITSUI FUDOSAN COMPANY LIMITED$JAPAN$6010001034957,1,645719,22.8772222222222,2179,32.2480230510692,1287,21.8772222222222,31.2480230510692,9.37080082884702
FREDERICK$MATTHEW$GOLTZ$1971$2,3.51,60556,25.4353333333333,1831,34.6923156826883,1149,21.9253333333333,31.1823156826883,9.25698234935495
OC343897,18,1781,22.2437777777778,2288,31.4839373881916,1339,4.24377777777778,13.4839373881916,9.24015961041386
"MITSUI & CO., LTD.$TOKYO, JAPAN$0100-01-008767",2,174235,3.978,64852,13.1056937212174,5403,1.978,11.1056937212174,9.12769372121744
AGNES$MARY$BARTON$1954$11,1.5056,423987,1.49044444444445,522171,10.5000000375751,8027,-0.0151555555555551,8.99440003757511,9.00955559313067
STEWART$JOHN$BAIRD$1971$6,1.4977,486982,1.50177777777778,457485,10.5000000826251,8026,0.00407777777777785,9.00230008262511,8.99822230484733
09223445,8,9761,105.484333333333,202,114.285513828357,187,97.4843333333334,106.285513828357,8.80118049502339
LONDON PENSIONS FUND AUTHORITY$NA$NA,3,124668,4.47844444444444,44617,13.2738780233112,5361,1.47844444444444,10.2738780233112,8.79543357886673
PIERRE-ANTOINE$NA$DE SELANCY$1971$7,1,1916920,11.3902222222222,7126,20.1008173766366,2638,10.3902222222222,19.1008173766366,8.71059515441439
KRISTEN$NA$ODENDAAL$1974$8,0.8324,2829267,5.71855555555556,27189,14.4122614737835,4709,4.88615555555556,13.5798614737835,8.69370591822793
DECLAN$NA$WALSH$1966$3,1,697237,1,685912,9.69015582182692,9456,0,8.69015582182692,8.69015582182692
1 participant_id sumdpi rankdpi sumnpi ranknpi sumtransitive ranktransitive diff_npi_dpi diff_transitive_dpi diff_transitive_npi
2 10657226 10 6219 342.955333333334 23 462.050947342302 19 332.955333333334 452.050947342302 119.095614008968
3 08885072 1 1226949 389.079222222222 19 468.031302647188 18 388.079222222222 467.031302647188 78.9520804249655
4 11443992 11 5149 591.460888888889 10 669.338549583877 9 580.460888888889 658.338549583877 77.8776606949871
5 SC095000 5 24872 670.525666666667 8 735.610780469834 7 665.525666666667 730.610780469834 65.0851138031673
6 03954113 0 3928492 0 3928492 56.3302557872759 564 0 56.3302557872759 56.3302557872759
7 00102498 18 1757 336.391666666667 26 377.785641323169 22 318.391666666667 359.785641323169 41.3939746565019
8 04220587 0 3938440 0 3938440 40.9288958121612 898 0 40.9288958121612 40.9288958121612
9 SURINDER$SINGH$TOOR$1972$3 2.5015 140665 39.3167777777778 947 73.9610142643602 357 36.8152777777778 71.4595142643602 34.6442364865824
10 02622406 1 953107 38.5817777777778 985 70.2113074441665 391 37.5817777777778 69.2113074441665 31.6295296663887
11 GARY$WILLIAM$TIPPER$1963$7 1.3341 536858 99.1909999999999 223 129.988376131723 146 97.8569 128.654276131723 30.7973761317235
12 SPECSAVERS OPTICAL SUPERSTORES LTD$UNITED KINGDOM$1721624 4 42441 1452.95022222222 1 1482.18842011308 1 1448.95022222222 1478.18842011308 29.2381978908597
13 RICHARD$LEONARD$SIMMONDS$1979$12 6.5138 15035 6.48166666666667 20445 35.4645679773307 1114 -0.0321333333333325 28.9507679773307 28.9829013106641
14 RUPERT$CHARLES GIFFORD$LYWOOD$1958$5 7.9889 10834 47.7837777777778 702 76.5569512712771 338 39.7948777777778 68.568051271277 28.7731734934993
15 ALEXA$KATE LOUISE CAMROUX$PEARMUND$1974$12 0.2554 3903961 122.389 164 150.791367871721 112 122.1336 150.535967871721 28.402367871721
16 MARK$NA$JOSPEH$1968$4 0 4034257 0 4034257 25.1249995937727 1853 0 25.1249995937727 25.1249995937727
17 HEINZ$HEINRICH$BAUER$1939$10 0 3971319 0 3971319 24.4692916321143 1966 0 24.4692916321143 24.4692916321143
18 BAJLINDER$KAUR$BOPARAN$1968$1 0 3961511 0 3961511 24.3750001727124 1972 0 24.3750001727124 24.3750001727124
19 OC326165 6 17447 103.840111111111 209 127.677935557153 150 97.8401111111111 121.677935557153 23.8378244460417
20 MATTHEW$JAMES$WOODS$1975$12 3.8241 59659 36.409 1084 58.7450903400284 538 32.5849 54.9209903400284 22.3360903400283
21 JAMES$RICHARD$CAMROUX-OLIVER$1967$9 0.2506 3909000 129.433666666667 144 150.791367871721 111 129.183066666667 150.540767871721 21.3577012050542
22 READE$NA$GRIFFITH$1965$4 1.4972 491331 636.465111111111 9 657.49955601355 10 634.967911111111 656.00235601355 21.0344449024385
23 JOHN$NA$MCDONAGH$1969$5 1 1427664 87.3861111111112 276 107.213226733802 198 86.3861111111112 106.213226733802 19.8271156226908
24 QATAR INVESTMENT AUTHORITY$QATAR$/ 0.9864 2818663 150.943333333333 114 170.469159583876 91 149.956933333333 169.482759583876 19.5258262505427
25 MICHELE$CAROLINE$GIDDENS$1965$9 0.9972 2793601 64.0042222222222 457 82.8732036087854 304 63.0070222222222 81.8760036087855 18.8689813865632
26 MINISTRY OF FINANCE$NA$NA 1 876006 1 846460 19.8318760999104 2774 0 18.8318760999104 18.8318760999104
27 SAMUEL$GEORGE ARMSTRONG$VESTEY$1941$3 1 593454 1 604909 19.1250009915149 2878 0 18.1250009915149 18.1250009915149
28 LAURENCE$JON$FUMAGALLI$1972$4 0.3379 3785704 37.7572222222222 1026 55.6425456988741 572 37.4193222222222 55.3046456988741 17.8853234766518
29 TAREQ$NA$NAQIB$1971$12 0 3948415 0 3948415 17.6250004758762 3357 0 17.6250004758762 17.6250004758762
30 11444019 6 17408 386.593444444445 20 403.985152490125 21 380.593444444445 397.985152490125 17.3917080456807
31 JENNIFER$CHRISTINE$LANCE$1966$9 0 3935050 0 3935050 16.7499169617751 3669 0 16.7499169617751 16.7499169617751
32 MICHAEL$JOSEPH$RYAN$1966$4 1 1431899 91.9212222222223 255 107.213226725418 199 90.9212222222223 106.213226725418 15.2920045031962
33 RONAN$NA$KILDUFF$1977$11 2 258052 40.3115555555556 909 55.5248600177933 575 38.3115555555556 53.5248600177933 15.2133044622377
34 JEAN-GUY$NA$DESJARDINS$1944$10 8 9585 165.875 88 180.731962006548 78 157.875 172.731962006548 14.8569620065477
35 03140521 35.5041 453 226.638222222222 55 241.120645742615 49 191.134122222222 205.616545742615 14.4824235203928
36 MANJIT$NA$DALE$1965$6 2.3176 162072 163.911666666667 92 178.248028826349 81 161.594066666667 175.930428826349 14.3363621596826
37 FREDERICK$PAUL$GRAHAM-WATSON$1957$9 0.6741 2838997 0.337333333333333 3651011 14.583333305857 4612 -0.336766666666667 13.909233305857 14.2459999725236
38 01142830 17.3204 1948 276.395222222222 35 290.62995167509 31 259.074822222222 273.30955167509 14.2347294528681
39 09405653 2.3244 161817 11.1937777777778 7225 25.270673368002 1841 8.86937777777778 22.946273368002 14.0768955902242
40 08286875 45.8382 268 271.165444444445 36 284.837428399735 35 225.327244444445 238.999228399736 13.6719839552909
41 LORRAINE$GERALDINE$SPENCER$1959$5 0.4936 3669613 0.491888888888889 3568226 14.1200884354501 4801 -0.001711111111111 13.6264884354501 13.6281995465612
42 DAVID$JEREMY$COURTENAY-STAMP$1962$4 0.4911 3727778 0.495222222222222 3462306 14.1200884354501 4800 0.00412222222222203 13.6289884354501 13.6248662132279
43 00395826 8 9152 107.014666666667 196 120.608813410091 167 99.0146666666666 112.608813410091 13.5941467434246
44 LEON$PAUL$JONES$1980$4 4.9752 33464 4.993 36314 18.564442877988 3069 0.0177999999999994 13.589242877988 13.571442877988
45 INFLEXION PARTNERSHIP CAPITAL FUND I GENERAL PARTNER GUERNSEY LIMITED (AS GP OF INFLEXION PARTNERSHIP CAPITAL FUND I GENERAL PARTNER GUERNSEY LP)$GUERNSEY$2075 0 4017857 0 4017857 13.4999998990969 5310 0 13.4999998990969 13.4999998990969
46 WILLIAM$BRUCE$KENDALL$1961$8 3.3652 68795 25.8097777777778 1799 39.2585890720939 949 22.4445777777778 35.8933890720939 13.4488112943161
47 EMILIO$NA$DI SPIEZIO SARDO$1977$3 0.4986 3404264 0.502333333333333 3035959 13.9507883608242 5119 0.00373333333333298 13.4521883608242 13.4484550274908
48 TRISTAN$NICHOLAS$RAMUS$1972$9 1.5078 415660 10.7518888888889 8051 24 1998 9.24408888888889 22.4922 13.2481111111111
49 STEPHEN$BERNARD$LILLEY$1968$4 0.3332 3834029 42.5912222222222 840 55.6425456988741 573 42.2580222222222 55.3093456988741 13.0513234766518
50 PETER$STEVEN CHRISTOPHER$BRODNICKI$1962$5 2 200423 40.178 913 53.145803755235 604 38.178 51.145803755235 12.967803755235
51 12242839 0 3952163 0 3952163 12.950317378398 5822 0 12.950317378398 12.950317378398
52 LO HOLDING SA$GENEVA, SWITZERLAND$CH-660.1.793.002-5 1 971706 19.2664444444445 2881 31.9039719623088 1325 18.2664444444445 30.9039719623088 12.6375275178643
53 ETL INTERNATIONAL AG$GERMANY$DE281293152 1 1101695 34.641 1163 47.1368207299801 720 33.641 46.1368207299801 12.4958207299801
54 ANN$HERON$GLOAG$1942$12 14.8211 2760 48.6741111111111 673 60.894495044748 507 33.8530111111111 46.073395044748 12.2203839336369
55 01417162 13 3477 320.993555555555 28 333.114660129009 27 307.993555555555 320.114660129009 12.121104573454
56 BARRY$MICHAEL$LAMBERT$1950$6 0.5063 2939590 0.487777777777778 3613444 12.5000001377942 5977 -0.018522222222222 11.9937001377942 12.0122223600164
57 ARES MANAGEMENT, LP$UNITED STATES$5434226 0 3978278 0 3978278 12.0000016961216 6231 0 12.0000016961216 12.0000016961216
58 ASHLEY$NA$SHAFFER$1998$6 0 3990947 0 3990947 11.8975784234647 6695 0 11.8975784234647 11.8975784234647
59 ANDREW$SIMON$DAVIS$1963$7 14.5042 2788 869.487555555556 6 881.3365356159 5 854.983355555556 866.8323356159 11.8489800603431
60 SCULPTOR FINANCE (CO) IRELAND DAC$IRELAND$IE505730 0 4001939 0 4001939 11.6249997005068 6844 0 11.6249997005068 11.6249997005068
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62 JOHN$ANDREW$GATLEY$1964$10 0.5029 3104410 1.48466666666667 527841 12.5623124763371 5969 0.981766666666668 12.0594124763371 11.0776458096704
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491
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algorithm,k,superholderpriority,recall
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npi,6,1,0.971201588877855
transitive_alpha0.0,6,0,0.388282025819265
transitive_alpha0.0,6,1,0.388282025819265
transitive_alpha0.1,6,0,0.924528301886792
transitive_alpha0.1,6,1,1
transitive_alpha0.2,6,0,0.924528301886792
transitive_alpha0.2,6,1,1
transitive_alpha0.3,6,0,0.925521350546177
transitive_alpha0.3,6,1,1
transitive_alpha0.4,6,0,0.925521350546177
transitive_alpha0.4,6,1,1
transitive_alpha0.5,6,0,0.930486593843098
transitive_alpha0.5,6,1,1
transitive_alpha0.6,6,0,0.930486593843098
transitive_alpha0.6,6,1,1
transitive_alpha0.7,6,0,0.930486593843098
transitive_alpha0.7,6,1,1
transitive_alpha0.8,6,0,0.94240317775571
transitive_alpha0.8,6,1,1
transitive_alpha0.9,6,0,0.990069513406157
transitive_alpha0.9,6,1,1
transitive_alpha0.999,6,0,0.998013902681231
transitive_alpha0.999,6,1,1
transitivedpi_alpha0.0,6,0,0.387288977159881
transitivedpi_alpha0.0,6,1,0.387288977159881
transitivedpi_alpha0.1,6,0,0.923535253227408
transitivedpi_alpha0.1,6,1,0.999006951340616
transitivedpi_alpha0.2,6,0,0.923535253227408
transitivedpi_alpha0.2,6,1,0.999006951340616
transitivedpi_alpha0.3,6,0,0.923535253227408
transitivedpi_alpha0.3,6,1,0.999006951340616
transitivedpi_alpha0.4,6,0,0.923535253227408
transitivedpi_alpha0.4,6,1,0.999006951340616
transitivedpi_alpha0.5,6,0,0.924528301886792
transitivedpi_alpha0.5,6,1,0.999006951340616
transitivedpi_alpha0.6,6,0,0.929493545183714
transitivedpi_alpha0.6,6,1,0.999006951340616
transitivedpi_alpha0.7,6,0,0.929493545183714
transitivedpi_alpha0.7,6,1,0.999006951340616
transitivedpi_alpha0.8,6,0,0.938430983118173
transitivedpi_alpha0.8,6,1,0.999006951340616
transitivedpi_alpha0.9,6,0,0.95630585898709
transitivedpi_alpha0.9,6,1,0.999006951340616
transitivedpi_alpha0.999,6,0,0.996027805362463
transitivedpi_alpha0.999,6,1,0.999006951340616
baseline,7,0,0.388282025819265
dpi,7,0,0.388282025819265
dpi,7,1,0.388282025819265
npi,7,0,0.971201588877855
npi,7,1,0.971201588877855
transitive_alpha0.0,7,0,0.388282025819265
transitive_alpha0.0,7,1,0.388282025819265
transitive_alpha0.1,7,0,0.941410129096326
transitive_alpha0.1,7,1,1
transitive_alpha0.2,7,0,0.941410129096326
transitive_alpha0.2,7,1,1
transitive_alpha0.3,7,0,0.941410129096326
transitive_alpha0.3,7,1,1
transitive_alpha0.4,7,0,0.941410129096326
transitive_alpha0.4,7,1,1
transitive_alpha0.5,7,0,0.946375372393247
transitive_alpha0.5,7,1,1
transitive_alpha0.6,7,0,0.946375372393247
transitive_alpha0.6,7,1,1
transitive_alpha0.7,7,0,0.946375372393247
transitive_alpha0.7,7,1,1
transitive_alpha0.8,7,0,0.953326713008937
transitive_alpha0.8,7,1,1
transitive_alpha0.9,7,0,0.997020854021847
transitive_alpha0.9,7,1,1
transitive_alpha0.999,7,0,1
transitive_alpha0.999,7,1,1
transitivedpi_alpha0.0,7,0,0.387288977159881
transitivedpi_alpha0.0,7,1,0.387288977159881
transitivedpi_alpha0.1,7,0,0.936444885799404
transitivedpi_alpha0.1,7,1,0.999006951340616
transitivedpi_alpha0.2,7,0,0.936444885799404
transitivedpi_alpha0.2,7,1,0.999006951340616
transitivedpi_alpha0.3,7,0,0.936444885799404
transitivedpi_alpha0.3,7,1,0.999006951340616
transitivedpi_alpha0.4,7,0,0.936444885799404
transitivedpi_alpha0.4,7,1,0.999006951340616
transitivedpi_alpha0.5,7,0,0.941410129096326
transitivedpi_alpha0.5,7,1,0.999006951340616
transitivedpi_alpha0.6,7,0,0.941410129096326
transitivedpi_alpha0.6,7,1,0.999006951340616
transitivedpi_alpha0.7,7,0,0.941410129096326
transitivedpi_alpha0.7,7,1,0.999006951340616
transitivedpi_alpha0.8,7,0,0.944389275074479
transitivedpi_alpha0.8,7,1,0.999006951340616
transitivedpi_alpha0.9,7,0,0.971201588877855
transitivedpi_alpha0.9,7,1,0.999006951340616
transitivedpi_alpha0.999,7,0,0.999006951340616
transitivedpi_alpha0.999,7,1,0.999006951340616
baseline,8,0,0.388282025819265
dpi,8,0,0.388282025819265
dpi,8,1,0.388282025819265
npi,8,0,0.971201588877855
npi,8,1,0.971201588877855
transitive_alpha0.0,8,0,0.388282025819265
transitive_alpha0.0,8,1,0.388282025819265
transitive_alpha0.1,8,0,0.951340615690169
transitive_alpha0.1,8,1,1
transitive_alpha0.2,8,0,0.951340615690169
transitive_alpha0.2,8,1,1
transitive_alpha0.3,8,0,0.951340615690169
transitive_alpha0.3,8,1,1
transitive_alpha0.4,8,0,0.951340615690169
transitive_alpha0.4,8,1,1
transitive_alpha0.5,8,0,0.967229394240318
transitive_alpha0.5,8,1,1
transitive_alpha0.6,8,0,0.967229394240318
transitive_alpha0.6,8,1,1
transitive_alpha0.7,8,0,0.969215491559086
transitive_alpha0.7,8,1,1
transitive_alpha0.8,8,0,0.978152929493545
transitive_alpha0.8,8,1,1
transitive_alpha0.9,8,0,0.999006951340616
transitive_alpha0.9,8,1,1
transitive_alpha0.999,8,0,1
transitive_alpha0.999,8,1,1
transitivedpi_alpha0.0,8,0,0.387288977159881
transitivedpi_alpha0.0,8,1,0.387288977159881
transitivedpi_alpha0.1,8,0,0.951340615690169
transitivedpi_alpha0.1,8,1,0.999006951340616
transitivedpi_alpha0.2,8,0,0.951340615690169
transitivedpi_alpha0.2,8,1,0.999006951340616
transitivedpi_alpha0.3,8,0,0.951340615690169
transitivedpi_alpha0.3,8,1,0.999006951340616
transitivedpi_alpha0.4,8,0,0.951340615690169
transitivedpi_alpha0.4,8,1,0.999006951340616
transitivedpi_alpha0.5,8,0,0.951340615690169
transitivedpi_alpha0.5,8,1,0.999006951340616
transitivedpi_alpha0.6,8,0,0.95630585898709
transitivedpi_alpha0.6,8,1,0.999006951340616
transitivedpi_alpha0.7,8,0,0.95630585898709
transitivedpi_alpha0.7,8,1,0.999006951340616
transitivedpi_alpha0.8,8,0,0.95630585898709
transitivedpi_alpha0.8,8,1,0.999006951340616
transitivedpi_alpha0.9,8,0,0.984111221449851
transitivedpi_alpha0.9,8,1,0.999006951340616
transitivedpi_alpha0.999,8,0,0.999006951340616
transitivedpi_alpha0.999,8,1,0.999006951340616
baseline,9,0,0.388282025819265
dpi,9,0,0.388282025819265
dpi,9,1,0.388282025819265
npi,9,0,0.971201588877855
npi,9,1,0.971201588877855
transitive_alpha0.0,9,0,0.388282025819265
transitive_alpha0.0,9,1,0.388282025819265
transitive_alpha0.1,9,0,0.959285004965243
transitive_alpha0.1,9,1,1
transitive_alpha0.2,9,0,0.959285004965243
transitive_alpha0.2,9,1,1
transitive_alpha0.3,9,0,0.959285004965243
transitive_alpha0.3,9,1,1
transitive_alpha0.4,9,0,0.959285004965243
transitive_alpha0.4,9,1,1
transitive_alpha0.5,9,0,0.982125124131082
transitive_alpha0.5,9,1,1
transitive_alpha0.6,9,0,0.982125124131082
transitive_alpha0.6,9,1,1
transitive_alpha0.7,9,0,0.983118172790467
transitive_alpha0.7,9,1,1
transitive_alpha0.8,9,0,0.995034756703079
transitive_alpha0.8,9,1,1
transitive_alpha0.9,9,0,1
transitive_alpha0.9,9,1,1
transitive_alpha0.999,9,0,1
transitive_alpha0.999,9,1,1
transitivedpi_alpha0.0,9,0,0.387288977159881
transitivedpi_alpha0.0,9,1,0.387288977159881
transitivedpi_alpha0.1,9,0,0.954319761668322
transitivedpi_alpha0.1,9,1,0.999006951340616
transitivedpi_alpha0.2,9,0,0.954319761668322
transitivedpi_alpha0.2,9,1,0.999006951340616
transitivedpi_alpha0.3,9,0,0.954319761668322
transitivedpi_alpha0.3,9,1,0.999006951340616
transitivedpi_alpha0.4,9,0,0.954319761668322
transitivedpi_alpha0.4,9,1,0.999006951340616
transitivedpi_alpha0.5,9,0,0.959285004965243
transitivedpi_alpha0.5,9,1,0.999006951340616
transitivedpi_alpha0.6,9,0,0.970208540218471
transitivedpi_alpha0.6,9,1,0.999006951340616
transitivedpi_alpha0.7,9,0,0.970208540218471
transitivedpi_alpha0.7,9,1,0.999006951340616
transitivedpi_alpha0.8,9,0,0.970208540218471
transitivedpi_alpha0.8,9,1,0.999006951340616
transitivedpi_alpha0.9,9,0,0.998013902681231
transitivedpi_alpha0.9,9,1,0.999006951340616
transitivedpi_alpha0.999,9,0,0.999006951340616
transitivedpi_alpha0.999,9,1,0.999006951340616
baseline,10,0,0.388282025819265
dpi,10,0,0.388282025819265
dpi,10,1,0.388282025819265
npi,10,0,0.971201588877855
npi,10,1,0.971201588877855
transitive_alpha0.0,10,0,0.388282025819265
transitive_alpha0.0,10,1,0.388282025819265
transitive_alpha0.1,10,0,0.973187686196624
transitive_alpha0.1,10,1,1
transitive_alpha0.2,10,0,0.973187686196624
transitive_alpha0.2,10,1,1
transitive_alpha0.3,10,0,0.973187686196624
transitive_alpha0.3,10,1,1
transitive_alpha0.4,10,0,0.971201588877855
transitive_alpha0.4,10,1,1
transitive_alpha0.5,10,0,0.998013902681231
transitive_alpha0.5,10,1,1
transitive_alpha0.6,10,0,0.998013902681231
transitive_alpha0.6,10,1,1
transitive_alpha0.7,10,0,0.998013902681231
transitive_alpha0.7,10,1,1
transitive_alpha0.8,10,0,0.998013902681231
transitive_alpha0.8,10,1,1
transitive_alpha0.9,10,0,1
transitive_alpha0.9,10,1,1
transitive_alpha0.999,10,0,1
transitive_alpha0.999,10,1,1
transitivedpi_alpha0.0,10,0,0.387288977159881
transitivedpi_alpha0.0,10,1,0.387288977159881
transitivedpi_alpha0.1,10,0,0.960278053624628
transitivedpi_alpha0.1,10,1,0.999006951340616
transitivedpi_alpha0.2,10,0,0.960278053624628
transitivedpi_alpha0.2,10,1,0.999006951340616
transitivedpi_alpha0.3,10,0,0.960278053624628
transitivedpi_alpha0.3,10,1,0.999006951340616
transitivedpi_alpha0.4,10,0,0.960278053624628
transitivedpi_alpha0.4,10,1,0.999006951340616
transitivedpi_alpha0.5,10,0,0.971201588877855
transitivedpi_alpha0.5,10,1,0.999006951340616
transitivedpi_alpha0.6,10,0,0.984111221449851
transitivedpi_alpha0.6,10,1,0.999006951340616
transitivedpi_alpha0.7,10,0,0.984111221449851
transitivedpi_alpha0.7,10,1,0.999006951340616
transitivedpi_alpha0.8,10,0,0.984111221449851
transitivedpi_alpha0.8,10,1,0.999006951340616
transitivedpi_alpha0.9,10,0,0.999006951340616
transitivedpi_alpha0.9,10,1,0.999006951340616
transitivedpi_alpha0.999,10,0,0.999006951340616
transitivedpi_alpha0.999,10,1,0.999006951340616
1 algorithm k superholderpriority recall
2 baseline 1 0 0.384309831181728
3 dpi 1 0 0.385302879841112
4 dpi 1 1 0.386295928500497
5 npi 1 0 0.893743793445879
6 npi 1 1 0.893743793445879
7 transitive_alpha0.0 1 0 0.384309831181728
8 transitive_alpha0.0 1 1 0.386295928500497
9 transitive_alpha0.1 1 0 0.385302879841112
10 transitive_alpha0.1 1 1 0.950347567030784
11 transitive_alpha0.2 1 0 0.385302879841112
12 transitive_alpha0.2 1 1 0.950347567030784
13 transitive_alpha0.3 1 0 0.386295928500497
14 transitive_alpha0.3 1 1 0.950347567030784
15 transitive_alpha0.4 1 0 0.386295928500497
16 transitive_alpha0.4 1 1 0.950347567030784
17 transitive_alpha0.5 1 0 0.399205561072493
18 transitive_alpha0.5 1 1 0.952333664349553
19 transitive_alpha0.6 1 0 0.405163853028798
20 transitive_alpha0.6 1 1 0.952333664349553
21 transitive_alpha0.7 1 0 0.407149950347567
22 transitive_alpha0.7 1 1 0.953326713008937
23 transitive_alpha0.8 1 0 0.483614697120159
24 transitive_alpha0.8 1 1 0.960278053624628
25 transitive_alpha0.9 1 0 0.491559086395233
26 transitive_alpha0.9 1 1 0.961271102284012
27 transitive_alpha0.999 1 0 0.491559086395233
28 transitive_alpha0.999 1 1 0.961271102284012
29 transitivedpi_alpha0.0 1 0 0.385302879841112
30 transitivedpi_alpha0.0 1 1 0.385302879841112
31 transitivedpi_alpha0.1 1 0 0.385302879841112
32 transitivedpi_alpha0.1 1 1 0.899702085402185
33 transitivedpi_alpha0.2 1 0 0.385302879841112
34 transitivedpi_alpha0.2 1 1 0.899702085402185
35 transitivedpi_alpha0.3 1 0 0.385302879841112
36 transitivedpi_alpha0.3 1 1 0.899702085402185
37 transitivedpi_alpha0.4 1 0 0.385302879841112
38 transitivedpi_alpha0.4 1 1 0.899702085402185
39 transitivedpi_alpha0.5 1 0 0.39622641509434
40 transitivedpi_alpha0.5 1 1 0.901688182720953
41 transitivedpi_alpha0.6 1 0 0.404170804369414
42 transitivedpi_alpha0.6 1 1 0.901688182720953
43 transitivedpi_alpha0.7 1 0 0.405163853028798
44 transitivedpi_alpha0.7 1 1 0.901688182720953
45 transitivedpi_alpha0.8 1 0 0.479642502482622
46 transitivedpi_alpha0.8 1 1 0.910625620655412
47 transitivedpi_alpha0.9 1 0 0.479642502482622
48 transitivedpi_alpha0.9 1 1 0.910625620655412
49 transitivedpi_alpha0.999 1 0 0.479642502482622
50 transitivedpi_alpha0.999 1 1 0.910625620655412
51 baseline 2 0 0.388282025819265
52 dpi 2 0 0.388282025819265
53 dpi 2 1 0.388282025819265
54 npi 2 0 0.95630585898709
55 npi 2 1 0.95630585898709
56 transitive_alpha0.0 2 0 0.388282025819265
57 transitive_alpha0.0 2 1 0.388282025819265
58 transitive_alpha0.1 2 0 0.609731876861966
59 transitive_alpha0.1 2 1 0.975173783515392
60 transitive_alpha0.2 2 0 0.609731876861966
61 transitive_alpha0.2 2 1 0.975173783515392
62 transitive_alpha0.3 2 0 0.610724925521351
63 transitive_alpha0.3 2 1 0.975173783515392
64 transitive_alpha0.4 2 0 0.612711022840119
65 transitive_alpha0.4 2 1 0.975173783515392
66 transitive_alpha0.5 2 0 0.655412115193645
67 transitive_alpha0.5 2 1 0.974180734856008
68 transitive_alpha0.6 2 0 0.66137040714995
69 transitive_alpha0.6 2 1 0.974180734856008
70 transitive_alpha0.7 2 0 0.664349553128103
71 transitive_alpha0.7 2 1 0.975173783515392
72 transitive_alpha0.8 2 0 0.715988083416088
73 transitive_alpha0.8 2 1 0.978152929493545
74 transitive_alpha0.9 2 0 0.736842105263158
75 transitive_alpha0.9 2 1 0.978152929493545
76 transitive_alpha0.999 2 0 0.739821251241311
77 transitive_alpha0.999 2 1 0.978152929493545
78 transitivedpi_alpha0.0 2 0 0.387288977159881
79 transitivedpi_alpha0.0 2 1 0.387288977159881
80 transitivedpi_alpha0.1 2 0 0.609731876861966
81 transitivedpi_alpha0.1 2 1 0.974180734856008
82 transitivedpi_alpha0.2 2 0 0.609731876861966
83 transitivedpi_alpha0.2 2 1 0.974180734856008
84 transitivedpi_alpha0.3 2 0 0.609731876861966
85 transitivedpi_alpha0.3 2 1 0.974180734856008
86 transitivedpi_alpha0.4 2 0 0.610724925521351
87 transitivedpi_alpha0.4 2 1 0.974180734856008
88 transitivedpi_alpha0.5 2 0 0.656405163853029
89 transitivedpi_alpha0.5 2 1 0.979145978152929
90 transitivedpi_alpha0.6 2 0 0.658391261171798
91 transitivedpi_alpha0.6 2 1 0.973187686196624
92 transitivedpi_alpha0.7 2 0 0.659384309831182
93 transitivedpi_alpha0.7 2 1 0.974180734856008
94 transitivedpi_alpha0.8 2 0 0.692154915590864
95 transitivedpi_alpha0.8 2 1 0.977159880834161
96 transitivedpi_alpha0.9 2 0 0.710029791459782
97 transitivedpi_alpha0.9 2 1 0.977159880834161
98 transitivedpi_alpha0.999 2 0 0.710029791459782
99 transitivedpi_alpha0.999 2 1 0.977159880834161
100 baseline 3 0 0.388282025819265
101 dpi 3 0 0.388282025819265
102 dpi 3 1 0.388282025819265
103 npi 3 0 0.971201588877855
104 npi 3 1 0.971201588877855
105 transitive_alpha0.0 3 0 0.388282025819265
106 transitive_alpha0.0 3 1 0.388282025819265
107 transitive_alpha0.1 3 0 0.786494538232373
108 transitive_alpha0.1 3 1 0.99304865938431
109 transitive_alpha0.2 3 0 0.786494538232373
110 transitive_alpha0.2 3 1 0.99304865938431
111 transitive_alpha0.3 3 0 0.787487586891758
112 transitive_alpha0.3 3 1 0.99304865938431
113 transitive_alpha0.4 3 0 0.788480635551142
114 transitive_alpha0.4 3 1 0.99304865938431
115 transitive_alpha0.5 3 0 0.808341608738828
116 transitive_alpha0.5 3 1 0.991062562065541
117 transitive_alpha0.6 3 0 0.811320754716981
118 transitive_alpha0.6 3 1 0.991062562065541
119 transitive_alpha0.7 3 0 0.815292949354518
120 transitive_alpha0.7 3 1 0.992055610724926
121 transitive_alpha0.8 3 0 0.843098311817279
122 transitive_alpha0.8 3 1 0.98609731876862
123 transitive_alpha0.9 3 0 0.862959285004965
124 transitive_alpha0.9 3 1 0.98609731876862
125 transitive_alpha0.999 3 0 0.867924528301887
126 transitive_alpha0.999 3 1 0.98609731876862
127 transitivedpi_alpha0.0 3 0 0.387288977159881
128 transitivedpi_alpha0.0 3 1 0.387288977159881
129 transitivedpi_alpha0.1 3 0 0.789473684210526
130 transitivedpi_alpha0.1 3 1 0.992055610724926
131 transitivedpi_alpha0.2 3 0 0.789473684210526
132 transitivedpi_alpha0.2 3 1 0.992055610724926
133 transitivedpi_alpha0.3 3 0 0.789473684210526
134 transitivedpi_alpha0.3 3 1 0.992055610724926
135 transitivedpi_alpha0.4 3 0 0.789473684210526
136 transitivedpi_alpha0.4 3 1 0.992055610724926
137 transitivedpi_alpha0.5 3 0 0.805362462760675
138 transitivedpi_alpha0.5 3 1 0.995034756703079
139 transitivedpi_alpha0.6 3 0 0.807348560079444
140 transitivedpi_alpha0.6 3 1 0.990069513406157
141 transitivedpi_alpha0.7 3 0 0.808341608738828
142 transitivedpi_alpha0.7 3 1 0.991062562065541
143 transitivedpi_alpha0.8 3 0 0.823237338629593
144 transitivedpi_alpha0.8 3 1 0.985104270109235
145 transitivedpi_alpha0.9 3 0 0.843098311817279
146 transitivedpi_alpha0.9 3 1 0.985104270109235
147 transitivedpi_alpha0.999 3 0 0.845084409136048
148 transitivedpi_alpha0.999 3 1 0.985104270109235
149 baseline 4 0 0.388282025819265
150 dpi 4 0 0.388282025819265
151 dpi 4 1 0.388282025819265
152 npi 4 0 0.971201588877855
153 npi 4 1 0.971201588877855
154 transitive_alpha0.0 4 0 0.388282025819265
155 transitive_alpha0.0 4 1 0.388282025819265
156 transitive_alpha0.1 4 0 0.867924528301887
157 transitive_alpha0.1 4 1 0.999006951340616
158 transitive_alpha0.2 4 0 0.867924528301887
159 transitive_alpha0.2 4 1 0.999006951340616
160 transitive_alpha0.3 4 0 0.872889771598808
161 transitive_alpha0.3 4 1 0.999006951340616
162 transitive_alpha0.4 4 0 0.872889771598808
163 transitive_alpha0.4 4 1 0.999006951340616
164 transitive_alpha0.5 4 0 0.876861966236346
165 transitive_alpha0.5 4 1 0.998013902681231
166 transitive_alpha0.6 4 0 0.87785501489573
167 transitive_alpha0.6 4 1 0.998013902681231
168 transitive_alpha0.7 4 0 0.87785501489573
169 transitive_alpha0.7 4 1 0.998013902681231
170 transitive_alpha0.8 4 0 0.89175769612711
171 transitive_alpha0.8 4 1 0.99304865938431
172 transitive_alpha0.9 4 0 0.933465739821251
173 transitive_alpha0.9 4 1 0.99304865938431
174 transitive_alpha0.999 4 0 0.966236345580933
175 transitive_alpha0.999 4 1 0.99304865938431
176 transitivedpi_alpha0.0 4 0 0.387288977159881
177 transitivedpi_alpha0.0 4 1 0.387288977159881
178 transitivedpi_alpha0.1 4 0 0.866931479642503
179 transitivedpi_alpha0.1 4 1 0.998013902681231
180 transitivedpi_alpha0.2 4 0 0.866931479642503
181 transitivedpi_alpha0.2 4 1 0.998013902681231
182 transitivedpi_alpha0.3 4 0 0.866931479642503
183 transitivedpi_alpha0.3 4 1 0.998013902681231
184 transitivedpi_alpha0.4 4 0 0.866931479642503
185 transitivedpi_alpha0.4 4 1 0.998013902681231
186 transitivedpi_alpha0.5 4 0 0.869910625620656
187 transitivedpi_alpha0.5 4 1 0.999006951340616
188 transitivedpi_alpha0.6 4 0 0.868917576961271
189 transitivedpi_alpha0.6 4 1 0.997020854021847
190 transitivedpi_alpha0.7 4 0 0.868917576961271
191 transitivedpi_alpha0.7 4 1 0.997020854021847
192 transitivedpi_alpha0.8 4 0 0.883813306852036
193 transitivedpi_alpha0.8 4 1 0.992055610724926
194 transitivedpi_alpha0.9 4 0 0.902681231380338
195 transitivedpi_alpha0.9 4 1 0.992055610724926
196 transitivedpi_alpha0.999 4 0 0.913604766633565
197 transitivedpi_alpha0.999 4 1 0.992055610724926
198 baseline 5 0 0.388282025819265
199 dpi 5 0 0.388282025819265
200 dpi 5 1 0.388282025819265
201 npi 5 0 0.971201588877855
202 npi 5 1 0.971201588877855
203 transitive_alpha0.0 5 0 0.388282025819265
204 transitive_alpha0.0 5 1 0.388282025819265
205 transitive_alpha0.1 5 0 0.906653426017875
206 transitive_alpha0.1 5 1 1
207 transitive_alpha0.2 5 0 0.906653426017875
208 transitive_alpha0.2 5 1 1
209 transitive_alpha0.3 5 0 0.908639523336644
210 transitive_alpha0.3 5 1 1
211 transitive_alpha0.4 5 0 0.908639523336644
212 transitive_alpha0.4 5 1 1
213 transitive_alpha0.5 5 0 0.916583912611718
214 transitive_alpha0.5 5 1 1
215 transitive_alpha0.6 5 0 0.916583912611718
216 transitive_alpha0.6 5 1 1
217 transitive_alpha0.7 5 0 0.916583912611718
218 transitive_alpha0.7 5 1 1
219 transitive_alpha0.8 5 0 0.925521350546177
220 transitive_alpha0.8 5 1 0.998013902681231
221 transitive_alpha0.9 5 0 0.972194637537239
222 transitive_alpha0.9 5 1 0.998013902681231
223 transitive_alpha0.999 5 0 0.99304865938431
224 transitive_alpha0.999 5 1 0.998013902681231
225 transitivedpi_alpha0.0 5 0 0.387288977159881
226 transitivedpi_alpha0.0 5 1 0.387288977159881
227 transitivedpi_alpha0.1 5 0 0.905660377358491
228 transitivedpi_alpha0.1 5 1 0.999006951340616
229 transitivedpi_alpha0.2 5 0 0.905660377358491
230 transitivedpi_alpha0.2 5 1 0.999006951340616
231 transitivedpi_alpha0.3 5 0 0.905660377358491
232 transitivedpi_alpha0.3 5 1 0.999006951340616
233 transitivedpi_alpha0.4 5 0 0.905660377358491
234 transitivedpi_alpha0.4 5 1 0.999006951340616
235 transitivedpi_alpha0.5 5 0 0.906653426017875
236 transitivedpi_alpha0.5 5 1 0.999006951340616
237 transitivedpi_alpha0.6 5 0 0.907646474677259
238 transitivedpi_alpha0.6 5 1 0.999006951340616
239 transitivedpi_alpha0.7 5 0 0.907646474677259
240 transitivedpi_alpha0.7 5 1 0.999006951340616
241 transitivedpi_alpha0.8 5 0 0.916583912611718
242 transitivedpi_alpha0.8 5 1 0.997020854021847
243 transitivedpi_alpha0.9 5 0 0.938430983118173
244 transitivedpi_alpha0.9 5 1 0.997020854021847
245 transitivedpi_alpha0.999 5 0 0.98609731876862
246 transitivedpi_alpha0.999 5 1 0.997020854021847
247 baseline 6 0 0.388282025819265
248 dpi 6 0 0.388282025819265
249 dpi 6 1 0.388282025819265
250 npi 6 0 0.971201588877855
251 npi 6 1 0.971201588877855
252 transitive_alpha0.0 6 0 0.388282025819265
253 transitive_alpha0.0 6 1 0.388282025819265
254 transitive_alpha0.1 6 0 0.924528301886792
255 transitive_alpha0.1 6 1 1
256 transitive_alpha0.2 6 0 0.924528301886792
257 transitive_alpha0.2 6 1 1
258 transitive_alpha0.3 6 0 0.925521350546177
259 transitive_alpha0.3 6 1 1
260 transitive_alpha0.4 6 0 0.925521350546177
261 transitive_alpha0.4 6 1 1
262 transitive_alpha0.5 6 0 0.930486593843098
263 transitive_alpha0.5 6 1 1
264 transitive_alpha0.6 6 0 0.930486593843098
265 transitive_alpha0.6 6 1 1
266 transitive_alpha0.7 6 0 0.930486593843098
267 transitive_alpha0.7 6 1 1
268 transitive_alpha0.8 6 0 0.94240317775571
269 transitive_alpha0.8 6 1 1
270 transitive_alpha0.9 6 0 0.990069513406157
271 transitive_alpha0.9 6 1 1
272 transitive_alpha0.999 6 0 0.998013902681231
273 transitive_alpha0.999 6 1 1
274 transitivedpi_alpha0.0 6 0 0.387288977159881
275 transitivedpi_alpha0.0 6 1 0.387288977159881
276 transitivedpi_alpha0.1 6 0 0.923535253227408
277 transitivedpi_alpha0.1 6 1 0.999006951340616
278 transitivedpi_alpha0.2 6 0 0.923535253227408
279 transitivedpi_alpha0.2 6 1 0.999006951340616
280 transitivedpi_alpha0.3 6 0 0.923535253227408
281 transitivedpi_alpha0.3 6 1 0.999006951340616
282 transitivedpi_alpha0.4 6 0 0.923535253227408
283 transitivedpi_alpha0.4 6 1 0.999006951340616
284 transitivedpi_alpha0.5 6 0 0.924528301886792
285 transitivedpi_alpha0.5 6 1 0.999006951340616
286 transitivedpi_alpha0.6 6 0 0.929493545183714
287 transitivedpi_alpha0.6 6 1 0.999006951340616
288 transitivedpi_alpha0.7 6 0 0.929493545183714
289 transitivedpi_alpha0.7 6 1 0.999006951340616
290 transitivedpi_alpha0.8 6 0 0.938430983118173
291 transitivedpi_alpha0.8 6 1 0.999006951340616
292 transitivedpi_alpha0.9 6 0 0.95630585898709
293 transitivedpi_alpha0.9 6 1 0.999006951340616
294 transitivedpi_alpha0.999 6 0 0.996027805362463
295 transitivedpi_alpha0.999 6 1 0.999006951340616
296 baseline 7 0 0.388282025819265
297 dpi 7 0 0.388282025819265
298 dpi 7 1 0.388282025819265
299 npi 7 0 0.971201588877855
300 npi 7 1 0.971201588877855
301 transitive_alpha0.0 7 0 0.388282025819265
302 transitive_alpha0.0 7 1 0.388282025819265
303 transitive_alpha0.1 7 0 0.941410129096326
304 transitive_alpha0.1 7 1 1
305 transitive_alpha0.2 7 0 0.941410129096326
306 transitive_alpha0.2 7 1 1
307 transitive_alpha0.3 7 0 0.941410129096326
308 transitive_alpha0.3 7 1 1
309 transitive_alpha0.4 7 0 0.941410129096326
310 transitive_alpha0.4 7 1 1
311 transitive_alpha0.5 7 0 0.946375372393247
312 transitive_alpha0.5 7 1 1
313 transitive_alpha0.6 7 0 0.946375372393247
314 transitive_alpha0.6 7 1 1
315 transitive_alpha0.7 7 0 0.946375372393247
316 transitive_alpha0.7 7 1 1
317 transitive_alpha0.8 7 0 0.953326713008937
318 transitive_alpha0.8 7 1 1
319 transitive_alpha0.9 7 0 0.997020854021847
320 transitive_alpha0.9 7 1 1
321 transitive_alpha0.999 7 0 1
322 transitive_alpha0.999 7 1 1
323 transitivedpi_alpha0.0 7 0 0.387288977159881
324 transitivedpi_alpha0.0 7 1 0.387288977159881
325 transitivedpi_alpha0.1 7 0 0.936444885799404
326 transitivedpi_alpha0.1 7 1 0.999006951340616
327 transitivedpi_alpha0.2 7 0 0.936444885799404
328 transitivedpi_alpha0.2 7 1 0.999006951340616
329 transitivedpi_alpha0.3 7 0 0.936444885799404
330 transitivedpi_alpha0.3 7 1 0.999006951340616
331 transitivedpi_alpha0.4 7 0 0.936444885799404
332 transitivedpi_alpha0.4 7 1 0.999006951340616
333 transitivedpi_alpha0.5 7 0 0.941410129096326
334 transitivedpi_alpha0.5 7 1 0.999006951340616
335 transitivedpi_alpha0.6 7 0 0.941410129096326
336 transitivedpi_alpha0.6 7 1 0.999006951340616
337 transitivedpi_alpha0.7 7 0 0.941410129096326
338 transitivedpi_alpha0.7 7 1 0.999006951340616
339 transitivedpi_alpha0.8 7 0 0.944389275074479
340 transitivedpi_alpha0.8 7 1 0.999006951340616
341 transitivedpi_alpha0.9 7 0 0.971201588877855
342 transitivedpi_alpha0.9 7 1 0.999006951340616
343 transitivedpi_alpha0.999 7 0 0.999006951340616
344 transitivedpi_alpha0.999 7 1 0.999006951340616
345 baseline 8 0 0.388282025819265
346 dpi 8 0 0.388282025819265
347 dpi 8 1 0.388282025819265
348 npi 8 0 0.971201588877855
349 npi 8 1 0.971201588877855
350 transitive_alpha0.0 8 0 0.388282025819265
351 transitive_alpha0.0 8 1 0.388282025819265
352 transitive_alpha0.1 8 0 0.951340615690169
353 transitive_alpha0.1 8 1 1
354 transitive_alpha0.2 8 0 0.951340615690169
355 transitive_alpha0.2 8 1 1
356 transitive_alpha0.3 8 0 0.951340615690169
357 transitive_alpha0.3 8 1 1
358 transitive_alpha0.4 8 0 0.951340615690169
359 transitive_alpha0.4 8 1 1
360 transitive_alpha0.5 8 0 0.967229394240318
361 transitive_alpha0.5 8 1 1
362 transitive_alpha0.6 8 0 0.967229394240318
363 transitive_alpha0.6 8 1 1
364 transitive_alpha0.7 8 0 0.969215491559086
365 transitive_alpha0.7 8 1 1
366 transitive_alpha0.8 8 0 0.978152929493545
367 transitive_alpha0.8 8 1 1
368 transitive_alpha0.9 8 0 0.999006951340616
369 transitive_alpha0.9 8 1 1
370 transitive_alpha0.999 8 0 1
371 transitive_alpha0.999 8 1 1
372 transitivedpi_alpha0.0 8 0 0.387288977159881
373 transitivedpi_alpha0.0 8 1 0.387288977159881
374 transitivedpi_alpha0.1 8 0 0.951340615690169
375 transitivedpi_alpha0.1 8 1 0.999006951340616
376 transitivedpi_alpha0.2 8 0 0.951340615690169
377 transitivedpi_alpha0.2 8 1 0.999006951340616
378 transitivedpi_alpha0.3 8 0 0.951340615690169
379 transitivedpi_alpha0.3 8 1 0.999006951340616
380 transitivedpi_alpha0.4 8 0 0.951340615690169
381 transitivedpi_alpha0.4 8 1 0.999006951340616
382 transitivedpi_alpha0.5 8 0 0.951340615690169
383 transitivedpi_alpha0.5 8 1 0.999006951340616
384 transitivedpi_alpha0.6 8 0 0.95630585898709
385 transitivedpi_alpha0.6 8 1 0.999006951340616
386 transitivedpi_alpha0.7 8 0 0.95630585898709
387 transitivedpi_alpha0.7 8 1 0.999006951340616
388 transitivedpi_alpha0.8 8 0 0.95630585898709
389 transitivedpi_alpha0.8 8 1 0.999006951340616
390 transitivedpi_alpha0.9 8 0 0.984111221449851
391 transitivedpi_alpha0.9 8 1 0.999006951340616
392 transitivedpi_alpha0.999 8 0 0.999006951340616
393 transitivedpi_alpha0.999 8 1 0.999006951340616
394 baseline 9 0 0.388282025819265
395 dpi 9 0 0.388282025819265
396 dpi 9 1 0.388282025819265
397 npi 9 0 0.971201588877855
398 npi 9 1 0.971201588877855
399 transitive_alpha0.0 9 0 0.388282025819265
400 transitive_alpha0.0 9 1 0.388282025819265
401 transitive_alpha0.1 9 0 0.959285004965243
402 transitive_alpha0.1 9 1 1
403 transitive_alpha0.2 9 0 0.959285004965243
404 transitive_alpha0.2 9 1 1
405 transitive_alpha0.3 9 0 0.959285004965243
406 transitive_alpha0.3 9 1 1
407 transitive_alpha0.4 9 0 0.959285004965243
408 transitive_alpha0.4 9 1 1
409 transitive_alpha0.5 9 0 0.982125124131082
410 transitive_alpha0.5 9 1 1
411 transitive_alpha0.6 9 0 0.982125124131082
412 transitive_alpha0.6 9 1 1
413 transitive_alpha0.7 9 0 0.983118172790467
414 transitive_alpha0.7 9 1 1
415 transitive_alpha0.8 9 0 0.995034756703079
416 transitive_alpha0.8 9 1 1
417 transitive_alpha0.9 9 0 1
418 transitive_alpha0.9 9 1 1
419 transitive_alpha0.999 9 0 1
420 transitive_alpha0.999 9 1 1
421 transitivedpi_alpha0.0 9 0 0.387288977159881
422 transitivedpi_alpha0.0 9 1 0.387288977159881
423 transitivedpi_alpha0.1 9 0 0.954319761668322
424 transitivedpi_alpha0.1 9 1 0.999006951340616
425 transitivedpi_alpha0.2 9 0 0.954319761668322
426 transitivedpi_alpha0.2 9 1 0.999006951340616
427 transitivedpi_alpha0.3 9 0 0.954319761668322
428 transitivedpi_alpha0.3 9 1 0.999006951340616
429 transitivedpi_alpha0.4 9 0 0.954319761668322
430 transitivedpi_alpha0.4 9 1 0.999006951340616
431 transitivedpi_alpha0.5 9 0 0.959285004965243
432 transitivedpi_alpha0.5 9 1 0.999006951340616
433 transitivedpi_alpha0.6 9 0 0.970208540218471
434 transitivedpi_alpha0.6 9 1 0.999006951340616
435 transitivedpi_alpha0.7 9 0 0.970208540218471
436 transitivedpi_alpha0.7 9 1 0.999006951340616
437 transitivedpi_alpha0.8 9 0 0.970208540218471
438 transitivedpi_alpha0.8 9 1 0.999006951340616
439 transitivedpi_alpha0.9 9 0 0.998013902681231
440 transitivedpi_alpha0.9 9 1 0.999006951340616
441 transitivedpi_alpha0.999 9 0 0.999006951340616
442 transitivedpi_alpha0.999 9 1 0.999006951340616
443 baseline 10 0 0.388282025819265
444 dpi 10 0 0.388282025819265
445 dpi 10 1 0.388282025819265
446 npi 10 0 0.971201588877855
447 npi 10 1 0.971201588877855
448 transitive_alpha0.0 10 0 0.388282025819265
449 transitive_alpha0.0 10 1 0.388282025819265
450 transitive_alpha0.1 10 0 0.973187686196624
451 transitive_alpha0.1 10 1 1
452 transitive_alpha0.2 10 0 0.973187686196624
453 transitive_alpha0.2 10 1 1
454 transitive_alpha0.3 10 0 0.973187686196624
455 transitive_alpha0.3 10 1 1
456 transitive_alpha0.4 10 0 0.971201588877855
457 transitive_alpha0.4 10 1 1
458 transitive_alpha0.5 10 0 0.998013902681231
459 transitive_alpha0.5 10 1 1
460 transitive_alpha0.6 10 0 0.998013902681231
461 transitive_alpha0.6 10 1 1
462 transitive_alpha0.7 10 0 0.998013902681231
463 transitive_alpha0.7 10 1 1
464 transitive_alpha0.8 10 0 0.998013902681231
465 transitive_alpha0.8 10 1 1
466 transitive_alpha0.9 10 0 1
467 transitive_alpha0.9 10 1 1
468 transitive_alpha0.999 10 0 1
469 transitive_alpha0.999 10 1 1
470 transitivedpi_alpha0.0 10 0 0.387288977159881
471 transitivedpi_alpha0.0 10 1 0.387288977159881
472 transitivedpi_alpha0.1 10 0 0.960278053624628
473 transitivedpi_alpha0.1 10 1 0.999006951340616
474 transitivedpi_alpha0.2 10 0 0.960278053624628
475 transitivedpi_alpha0.2 10 1 0.999006951340616
476 transitivedpi_alpha0.3 10 0 0.960278053624628
477 transitivedpi_alpha0.3 10 1 0.999006951340616
478 transitivedpi_alpha0.4 10 0 0.960278053624628
479 transitivedpi_alpha0.4 10 1 0.999006951340616
480 transitivedpi_alpha0.5 10 0 0.971201588877855
481 transitivedpi_alpha0.5 10 1 0.999006951340616
482 transitivedpi_alpha0.6 10 0 0.984111221449851
483 transitivedpi_alpha0.6 10 1 0.999006951340616
484 transitivedpi_alpha0.7 10 0 0.984111221449851
485 transitivedpi_alpha0.7 10 1 0.999006951340616
486 transitivedpi_alpha0.8 10 0 0.984111221449851
487 transitivedpi_alpha0.8 10 1 0.999006951340616
488 transitivedpi_alpha0.9 10 0 0.999006951340616
489 transitivedpi_alpha0.9 10 1 0.999006951340616
490 transitivedpi_alpha0.999 10 0 0.999006951340616
491 transitivedpi_alpha0.999 10 1 0.999006951340616

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