Faster algorithms for computing power indices in weighted voting games

Abstract

We consider weighted voting games with n players. We show how to compute the Banzhaf power index for every player within a running time of O( n 2 1.415 n ), and how to compute the Shapley–Shubik power index within a running time of O( n 1.415 n ). Our result improves on the straightforward running times of O( n 2 2 n ) and O( n 2 n ), respectively, that are implicit in the definitions of these power indices.