Computing Power Indices for Large Voting Games

Voting Power Indices enable the analysis of the distribution of power in a legislature or voting body in which different members have different numbers of votes. Although this approach to the measurement of power, based on co-operative game theory, has been known for a long time its empirical application has been to some extent limited, in part by the difficulty of computing the indices when there are many players. This paper presents new algorithms for computing the power indices of Shapley and Shubik and of Banzhaf, that are essentially modifications of approximation methods due to Owen, and have been shown to work well in real applications. They are of most utility in situations where both the number of players is large and their voting weights are very concentrated, some members having considerably larger numbers of votes than others, where Owen's approximation methods are least accurate. JEL Classification numbers: C63, C71, D71, D72