Generating functions partitioning algorithm for computing power indices in weighted voting games

In this paper new approach to calculating power indices is described. The problem com­ plexity class is #P-complete. Constructed algorithm is a mix of ideas of two algorithms: Klinz & Woeginger partitioning algorithm and Mann & Shapley generating functions al­ gorithm. Time and space complexities of the algorithm are analysed and compared with other known algorithms for the problem. Constructed algorithm has pessimistic time com­ plexity O n2  and pseudopolynomial complexity O nq , where q is quota of the voting game. This paper also solves open problem stated in [2] existence of the algorithm for calculating Banzhaf power indices of all players with time complexity lower than O n 2  . Not only is the answer positive but this can be done keeping the pseudopolynomial com­ plexity of generating functions algorithm in case weights are integers. New open problems are stated.