Power Indices and minimal winning Coalitions

TL;DR

This paper introduces a new combinatorial formula for calculating the Penrose-Banzhaf and Shapley-Shubik power indices using only the set of minimal winning coalitions, simplifying the computation process.

Contribution

The paper presents a novel combinatorial approach to compute power indices solely from minimal winning coalitions, enhancing efficiency and understanding.

Findings

New formula simplifies power index calculations

Applicable to various voting game analyses

Improves computational efficiency for political power measurement

Abstract

The Penrose-Banzhaf index and the Shapley-Shubik index are the best-known and the most used tools to measure political power of voters in simple voting games. Most methods to calculate these power indices are based on counting winning coalitions, in particular those coalitions a voter is decisive for. We present a new combinatorial formula how to calculate both indices solely using the set of minimal winning coalitions.