Monte Carlo Methods for the Shapley–Shubik Power Index

Yuto Ushioda, Masato Tanaka and Tomomi Matsui
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Yuto Ushioda: Graduate School of Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Masato Tanaka: Graduate School of Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
Tomomi Matsui: Graduate School of Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan

Games, 2022, vol. 13, issue 3, 1-14

Abstract: This paper deals with the problem of calculating the Shapley–Shubik power index in weighted majority games. We propose an efficient Monte Carlo algorithm based on an implicit hierarchical structure of permutations of players. Our algorithm outputs a vector of power indices preserving the monotonicity, with respect to the voting weights. We show that our algorithm reduces the required number of samples, compared with the naive algorithm.

Keywords: voting game; weighted majority game; power index; Monte Carlo algorithm (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2022
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