In this paper, we propose fast pseudo-polynomial-time algorithms for computing power indices in weighted majority games. We show that we can compute the Banzhaf index for all players in $O(n+q\log (q))$ time, where $n$ is the number of players and $q$ is a given quota. Moreover, we prove that the Shapley--Shubik index for all players can be computed in $O(nq\log (q))$ time. Our algorithms are faster than existing algorithms when $q=2^{o(n)}$. Our algorithms exploit efficient computation techniques for formal power series.

翻译：本文提出了计算加权多数博弈中权力指数的快速伪多项式时间算法。我们证明了所有参与者的班扎夫指数可在$O(n+q\log (q))$时间内计算，其中$n$为参与者数量，$q$为给定配额。此外，我们证明了所有参与者的夏普利-舒比克指数可在$O(nq\log (q))$时间内计算。当$q=2^{o(n)}$时，我们的算法优于现有算法。这些算法利用了形式幂级数的高效计算技术。