Consistent approval-based multi-winner rules

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., fixed-size group candidates, based on approval ballots. We introduce the class ABC scoring and provide characterization this consistency axiom. Building upon result, we axiomatically characterize three important rules: Proportional Approval Voting, Multi-Winner Voting Chamberlin–Courant rule. Our results demonstrate variety illustrate different, orthogonal principles may represent: proportionality, diversity, individual excellence.