Monte Carlo Methods for Calculating Shapley-Shubik Power Index in Weighted Majority Games

TL;DR

This paper develops and analyzes Monte Carlo algorithms to efficiently compute the Shapley-Shubik power index in weighted majority games, reducing computational effort compared to naive methods.

Contribution

It introduces an improved Monte Carlo algorithm that decreases the number of samples needed for accurate power index calculation in weighted majority games.

Findings

The naive Monte Carlo algorithm's sample size requirements are analyzed.

The proposed algorithm significantly reduces the number of samples needed.

Experimental results demonstrate improved efficiency over naive methods.

Abstract

This paper addresses Monte Carlo algorithms for calculating the Shapley-Shubik power index in weighted majority games. First, we analyze a naive Monte Carlo algorithm and discuss the required number of samples. We then propose an efficient Monte Carlo algorithm and show that our algorithm reduces the required number of samples as compared to the naive algorithm.