Computing power indices for weighted voting games via dynamic programming

We study the efficient computation of power indices for weighted voting games using the para- digm of dynamic programming. We survey the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices and point out how these approaches carry over to related power indices. Within a unified framework, we present new efficient algorithms for the Public Good index and a recently proposed power index based on minimal winning coalitions of the smallest size, as well as a very first method for computing the Johnston indices for weighted voting games efficiently. We introduce a software package providing fast C++ implementations of all the power indices mentioned in this article, discuss computing times, as well as storage requirements.