Computing power indices in weighted multiple majority games. (Q1402487)

The authors present a method of computing the Banzhaf index and the Shapley-Shubik index efficiently by using generating functions for weighted multiple majority games and analyze its temporal complexity. See also the articles by \textit{S. J. Brams} and \textit{Affuso} [Theory and Decision 7, 29--56 (1976)] and \textit{A. Tannenbaum} [The Mathematica Journal 7, 58--63 (1997)] in this connection. The authors also apply the algorithms obtained to compute both the Banzhaf index and the Shapley-Shubik index under the two decision rules adopted in the Nice European Union Summit.