Axiomatic characterizations of consistent approval-based committee choice rules

TL;DR

This paper provides axiomatic characterizations of key approval-based multiwinner voting rules, including Proportional Approval Voting and Chamberlin--Courant, emphasizing the role of the consistency property in their definitions.

Contribution

It offers the first axiomatic characterizations of several important approval-based committee rules, highlighting the significance of the consistency axiom.

Findings

Characterizations of Proportional Approval Voting and Chamberlin--Courant

Identification of the consistency axiom as central to these rules

Clarification of the axiomatic foundations of Thiele methods

Abstract

We prove axiomatic characterizations of several important multiwinner rules within the class of approval-based committee choice rules. These are voting rules that return a set of (fixed-size) committees. In particular, we provide axiomatic characterizations of Proportional Approval Voting, the Chamberlin--Courant rule, and other Thiele methods. These rules share the important property that they satisfy an axiom called consistency, which is crucial in our characterizations.