Axiomatic Characterization of Committee Scoring Rules

TL;DR

This paper provides an axiomatic characterization of committee scoring rules, a broad class of multiwinner preference aggregation methods, using four standard axioms plus a new committee dominance axiom, supported by novel theoretical techniques.

Contribution

It introduces and axiomatizes multiwinner decision scoring rules, extending the understanding of preference aggregation beyond single-winner rules.

Findings

Committee scoring rules are characterized by four axioms plus committee dominance.

The paper develops new notions and techniques for axiomatic characterization.

Multiwinner decision scoring rules generalize the majority relation.

Abstract

Committee scoring rules form a rich class of aggregators of voters' preferences for the purpose of selecting subsets of objects with desired properties, e.g., a shortlist of candidates for an interview, a representative collective body such as a parliament, or a set of locations for a set of public facilities. In the spirit of celebrated Young's characterization result that axiomatizes single-winner scoring rules, we provide an axiomatic characterization of multiwinner committee scoring rules. We show that committee scoring rules---despite forming a remarkably general class of rules---are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by one axiom specific to multiwinner rules which we call committee dominance. In the course of our proof, we develop several new notions and techniques. In particular, we introduce and axiomatically characterize multiwinner decision scoring rules, a class of rules that broadly generalizes the well-known majority relation.