The power of the largest player

TL;DR

This paper examines various power indices in weighted voting games, focusing on the maximum influence a non-dictatorial player can have, and classifies these indices into two distinct categories.

Contribution

It provides a novel analysis of how different power indices compare in terms of the largest possible power for non-dictatorial players, offering guidance for index selection.

Findings

Power indices can be divided into two classes based on maximum influence.

This classification aids in choosing appropriate indices for applications.

The analysis enhances understanding of influence measurement in weighted games.

Abstract

Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This paper analyzes how power indices differ with respect to the largest possible power of a non-dictatorial player. It turns out that the considered set of power indices can be partitioned into two classes. This may serve as another indication which index to use in a given application.