Power in Weighted Voting Systems

Volume 7, Issue 1
Winter 1997

Traditional algorithms for computing either the Banzhaf or the Shapley-Shubik power index of a voter in a n-voter weighted voting system are based on some type of search through the subsets of an n-set or the permutations of an n-set, respectively, and only work for small values of n. This paper presents an approach based on generating functions, with which the Banzhaf and Shapley-Shubik power distributions can be computed even when the value of n is large. To illustrate the computations, the power distributions of the U.S. Electoral College are examined.