Title: Consistent Approval-Based Multi-Winner Rules,
Abstract: 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 multi-winner 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 multi-winner voting rules may represent:
individual excellence, diversity, and proportionality.