Allocation Proportionality of OWA--Based Committee Scoring Rules

While proportionality is frequently named as a desirable property of voting rules, its interpretation in multiwinner voting differs significantly from that in apportionment. We aim to bridge these two distinct notions of proportionality by introducing the concept of allocation proportionality, founded upon the framework of party elections, where each candidate in a multiwinner election is assigned to a party. A voting rule is allocation proportional if each party's share of elected candidates equals that party's aggregate score. Recognizing that no committee scoring rule can universally satisfy allocation proportionality in practice, we introduce a new measure of allocation proportionality degree and discuss how it relates to other quantitative measures of proportionality. This measure allows us to compare OWA-based committee scoring rules according to how much they diverge from the ideal of allocation proportionality. We present experimental results for several common rules: SNTV, $k$-Borda, Chamberlin-Courant, Harmonic Borda, Proportional $k$-Approval Voting, and Bloc Voting.