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.
Additional Information:
This paper is an extended version of our paper published in the 21st Japan-Korea Joint Workshop on Algorithms and Computation (WAAC), Fukuoka, Japan, 26–27 August 2018.