Consistent Approval-Based Multi-Winner Rules

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