Tuesday, March 13, 2012

Shapley-Shubik Power Index in R

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:


# 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.


  1. I did the same without combining constituencies, and the result are pretty much the same - #2 seems to be really under-represented.
    On the other hand the student constituency seems to have really high relative power.

  2. HI there: Two questions: 1) do the permutations need to match the number of constituencies in the variable constit? 2) Is the number 107 the number required to win the election?