The Expanding Approvals Rule: Improving Proportional Representation and Monotonicity

TL;DR

This paper introduces the Expanding Approvals Rule (EAR), a new voting method that enhances proportional representation and monotonicity, addressing limitations of traditional methods like STV.

Contribution

The paper proposes EAR, a novel voting rule that improves upon STV by satisfying stronger PR and monotonicity properties, and efficiently handling indifferences.

Findings

EAR satisfies stronger PR axioms than STV.

EAR handles indifferences efficiently.

EAR exhibits improved candidate monotonicity.

Abstract

Proportional representation (PR) is often discussed in voting settings as a major desideratum. For the past century or so, it is common both in practice and in the academic literature to jump to single transferable vote (STV) as the solution for achieving PR. Some of the most prominent electoral reform movements around the globe are pushing for the adoption of STV. It has been termed a major open problem to design a voting rule that satisfies the same PR properties as STV and better monotonicity properties. In this paper, we first present a taxonomy of proportional representation axioms for general weak order preferences, some of which generalise and strengthen previously introduced concepts. We then present a rule called Expanding Approvals Rule (EAR) that satisfies properties stronger than the central PR axiom satisfied by STV, can handle indifferences in a convenient and computationally efficient manner, and also satisfies better candidate monotonicity properties. In view of this, our proposed rule seems to be a compelling solution for achieving proportional representation in voting settings.