# ShapleyShubik: Shapley Shubik Power Index In GameTheory: Cooperative Game Theory

## Description

This function computes Shapley - Shubik Power Index of a coalition.

## Usage

 `1` ```ShapleyShubik(quota, y, Names = NULL) ```

## Arguments

 `quota` Minimum amount of votes to pass a vote `y` Seats of every party `Names` Labels of the parties

## Details

The Shapley and Shubik index works as follows. There is a group of individuals all willing to vote on a proposal. They vote in order and as soon as a majority has voted for the proposal, it is declared passed and the member who voted last is given credit for having passed it. Let us consider that the members are voting randomly. Then we compute the frequency with which an individual is the one that gets the credit for passing the proposal. That measures the number of times that the action of that individual joining the coalition of their predecessors makes it a winning coalition. Note that if this index reaches the value of 0, then it means that this player is a dummy. When the index reaches the value of 1, the player is a dictator.

## Author(s)

Sebastian Cano-Berlanga <[email protected]>

## References

Shapley L, Shubik M (1954). "A Method for Evaluating the Distribution of Power in a Committee System." The American Political Science Review, 48(3), 787–792.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```## SHAPLEY - SHUBIK POWER INDEX APPLIED TO THE CATALAN PARLIAMENT # 2012 Elections SEATS<-c(50,20,21,19,13,9,3) PARTIES<-c("CiU","PSC","ERC","PP","ICV","C's","CUP") E2012<-ShapleyShubik(68,SEATS,PARTIES) summary(E2012) # Results for 2012 elections # CiU PSC ERC PP ICV C's CUP # Votes 50.000 20.000 21.000 19.000 13.0000 9.0000 3.0000 # Votes (R) 0.370 0.148 0.156 0.141 0.0963 0.0667 0.0222 # Shapley-Shubik 0.533 0.133 0.133 0.133 0.0333 0.0333 0.0000 ```

GameTheory documentation built on July 4, 2017, 5:02 p.m.