A Recursive Measure of Voting Power that Satisfies Reasonable Postulates

TL;DR

This paper introduces a new recursive voting power measure that accounts for partial efficacy and satisfies key postulates, advancing the theoretical understanding of voting power analysis.

Contribution

It proposes a novel recursive measure of voting power based on partial efficacy, satisfying multiple desirable postulates, unlike classical measures.

Findings

The measure satisfies iso-invariance, dummy, dominance, donation, minimum-power bloc, and quarrel postulates.

Representation of voting games using division lattice and stochastic processes supports the measure's viability.

The measure extends classical voting power concepts by incorporating partial efficacy.

Abstract

We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice and via the notion of random walks in stochastic processes, and show the viability of our recursive measure by proving it satisfies a plethora of postulates that any reasonable voting measure should satisfy. These include the iso-invariance, dummy, dominance, donation, minimum-power bloc, and quarrel postulates.