EPIC R Package - Efficient Power Index Computation

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Setup

Prerequisites

R, RStudio IDE, C++ Compiler, GNU make, GMP (Gnu Multiple Precision Arithmetic Library), Autoconf, Git (optional)

Prerequisites for Windows

• Download and install Rtools

Prerequisites for Linux

• All the needed tools can be installed using the distributions package manager (e.g. for apt package manager run: apt install gcc git make libgmp-dev).

Installation

1. Download the repository. This can be done in two different ways:

   1. Clone the repository using git (git clone ...)
   2. Download the repository as ZIP archive using the download dropdown menu on the Repository overview. The archive must get extracted after download.

2. For Linux: Run autoconf in the repository to generate the configure file from the configure.ac template. Then run ./configure.

   It is also possible to manually create the Makevars file by adding the following contents and inserting the path to the GMP installation:

   GMP_DIR = *Insert the path to your GMP directory here*
   
   CXX_STD=@CXX_STD@ 
   
   PKG_LIBS = -L$(GMP_DIR)/.libs -lgmpxx -lgmp
   

3. This directory can be opened in R Studio as a project: "File" -> "Open Project" -> Navigate to the downloaded repository -> Open "EfficientPowerIndices.Rproj"

4. Now the R package can be built and installed in the upper left hand side in the "Build" Tab using the "Install and Restart" button.

Usage

After installing, the package can be included in R Scripts using library(EfficientPowerIndices)

The R package offers the function ComputePowerIndex which expects the following parameters:

Required parameters

name	type	description
index	index shortcut as String (see Available indices)	the index to compute
weights or weightsfile	numeric vector or .csv file	the player weights for the weighted voting Game (*1)
quota	numeric	the quota for the weighted voting Game (*2)

(*1) The weights must be specified either by a numeric vector or a .csv file. The .csv file must contain one weight per line. The weights must all be integers unless you set the inputFloatWeights flag.

(*2) When setting the quota to 0, the first line of the weights file will be interpreted as the quota to use.

Optional parameters

name	type	description
precoalitions	List of integer vectors	specifies the structure of the precoalitions (*3)
verbose	boolean	adds extra output
filterNullPlayers	boolean	excludes null player from the calculation (not compatible with all indices!)
weightedMajorityGame	boolean	uses a weighted majority game (i.e. the weight sum must be greater than the quota for a coalition to be considered a winning coalition) for the underlying calculations
useGMPTypes	boolean	return the results as GNU MPFR types
inputFloatWeights	boolean	reads the weights from the weightfile as floating point numbers

(*3) When the weights are specified using a weightsfile the structure of the precoalitions will be generated from this file and the precoalitions specified using the parameter will be ignored. The weightsfile has to be written accordingly. If defined in the weightsfile, the players in the same precoalition should all be in the same line and seperated by ",". A new line is a new precoalition.

When using the precoalitions parameter the precoalitions are structured using a list of integer vectors. Player numbers are from 1 to n. For example precoalitions = list(c(1,3), c(2,4), c(5)) would be a preacoalition between player 1 and 3, player 2 and 4 while player 5 is alone.

Available indices

shortcut	name
ABZ	Absolute Banzhaf
APG	Absolute Public Good
APIG	Absolute Power Index G (based on the Dubey-Shapley identity)
BZ	Banzhaf
BO	Banzhaf Owen
BZB	Banzhaf from below
CC	Coleman Collective
CI	Coleman Initiative
CP	Coleman Preventive
DP	Deegan Packel
FT	Felsenthal
HN	Harsanyi Nash
J	Johnston
KB	Koenig Braeuninger (based on the Dubey-Shapley identity)
KBPH	Koenig Braeuninger (based on Raw Public Help Theta)
N	Nevison (based on the Dubey-Shapley identity)
NPH	Nevison (based on Raw Public Help Theta)
O	Owen
OPGI	Owen Extended PGI
PG	Public Good
PHT	Public Help Theta (based on the Dubey-Shapley identity)
PHTPH	Public Help Theta (based on Raw Public Help Theta)
PHX	Public Help Xi
PIF	Power Index F
PIG	Power Index G (based on the Dubey-Shapley identity)
PIGPH	Power Index G (based on Raw Public Help Theta)
RA	Rae
RBZ	Raw Banzhaf
RBZB	Raw Banzhaf from below
RDP	Raw Deegan Packel
RFT	Raw Felsenthal
RJ	Raw Johnston
RPG	Raw Public Good
RPHT	Raw Public Help Theta
RPHTSD	Raw Public Help Theta (based on the Dubey-Shapley identity)
RPIG	Raw Power Index G
RPIF	Raw Power Index F
RSH	Raw Shapley Shubik
SCB	Symmetric Coalitional Banzhaf
RSHB	Raw Shapley Shubik from below
SH	Shapley Shubik
SHB	Shapley Shubik from below
SPGI	Solidarity Public Good Index
T	Tijs
TPGI1	Threat Public Good Index 1
TPGI2	Threat Public Good Index 2
TPGI3	Threat Public Good Index 3
UPGI	Union Public Good Index
W	Number of winning coalitions
WM	Number of minimal winning coalitions
WS	Number of minimal winning coalitions of smallest cardinality

Example

For a simple example we want to calculate the Banzhaf index for a simple 5-player Game with the weights (9, 5, 3, 1, 1) and quota 11.

library(EfficientPowerIndices)

ComputePowerIndex(index = "BZ", quota = 11, weights = c(9, 5, 3, 1, 1), verbose = TRUE)

By setting the verbose parameter to TRUE we get extra output like the raw Banzhaf values and the total number of swings (sum over the raw Banzhaf values).