Axiomatic characterizations of consistent approval-based committee choice rules

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.

We were made aware of a gap in the proof of Theorem 1 (we do not show transitivity of the constructed ranking, Def. 1). We withdraw the paper for now