# Shapley-Shubik Power Index in R

March 13, 2012
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This spring we have Rector Elections at Warsaw School of Economics. One of my collegues Tomasz Szapiro agreed to start in the elections. This induced me to write Shapley-Shubik Power Index calculation snippet in R.
Rector elections in Warsaw School of Economics are organized in eleven constituencies representing different communities of our school. Each constituency is represented by different number of electors. I have written a simple R code calculating relative power of electors representing those constituencies. To reduce the volume of calculations I have joined some constituencies (6 and 7, 8 and 9, 10 and 11).

Here is the code performing the Shapley-Shubik Power Index calculations:

library(gregmisc)

# number of electors in each constituency
const <- c(30, 22, 27, 27, 41, + 11, 38 + 5, 1 + 9)

perms <- permutations(8, 8)
outcome <- apply(perms, 1, function(x) {
x[sum(cumsum(const[x]) < 107) + 1] })

sspi <- prop.table(table(outcome))
names(sspi) <- c(“C_1”,“C_2”, “C_3”, “C_4”, “C_5”,
“C_67”, “C_89”, “C_1011”)
plot(sspi / (const / sum(const)),
xlab=“constituency”, ylab=“power index / votes”)

The plot generated by the code shows relative power of constituency to number of its votes. Here it goes:

Interestingly relative power index of almost all constituencies is balanced. However, power index of constituency #2 is very low in comparison to the fraction of electors it possesses.

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