Approximation of Banzhaf indices and its application to voting games

TL;DR

This paper introduces an improved Banzhaf power index considering mutual persuasion among voters, applied to EU voting based on immigration data, and offers enhanced Monte Carlo approximation bounds.

Contribution

It proposes a novel power index incorporating mutual persuasion, applied to EU voting, with improved approximation bounds for Monte Carlo methods.

Findings

The new index accounts for mutual persuasion among voters.

Application to EU voting data based on immigration.

Enhanced bounds for Monte Carlo approximation methods.

Abstract

In this paper, we propose an improved version of the power index related to the Banzhaf power index for weighted voting systems. This index now takes into account the mutual persuasion power matrix(PPM) existing among the voters. This improved index is calculated for European Union voting by basing the PPM on immigration data among the EU countries. We also provide better approximation bounds for the Monte Carlo approximation method for computing power indices.