Axiomatic Characterization of Committee Scoring Rules

We provide an axiomatic characterization of committee scoring rules, analogues of the scoring rules for the multiwinner elections. We show that committee scoring rules are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by two axioms specific to multiwinner rules, committee neutrality and committee dominance. In the course of our proof, we develop several new notions. In particular, we introduce and characterize decision rules, a notion that may be useful on its own.