Consistent approval-based multi-winner rules

Abstract

This paper is an axiomatic study of consistent approval-based committee (ABC) rules. These are multi-winner voting rules that select a committee, i.e., a fixed-size group of candidates, based on approval ballots. We introduce the class of ABC scoring rules and provide an axiomatic characterization of this class based on the consistency axiom. Building upon this result, we axiomatically characterize three important consistent multi-winner rules: Proportional Approval Voting, Multi-Winner Approval Voting and the Approval Chamberlin–Courant rule. Our results demonstrate the variety of ABC scoring rules and illustrate three different, orthogonal principles that multi-winner voting rules may represent: proportionality, diversity, and individual excellence.