Allocation Proportionality of OWA--Based Committee Scoring Rules

TL;DR

This paper introduces the concept of allocation proportionality in multiwinner voting, proposing a new measure to evaluate how well different rules approximate this property, supported by experimental comparisons.

Contribution

It defines allocation proportionality for multiwinner rules, introduces a new measure for its degree, and compares several rules based on this measure.

Findings

No committee scoring rule fully satisfies allocation proportionality.

The new measure effectively quantifies divergence from ideal proportionality.

Experimental results show varying degrees of proportionality among common rules.

Abstract

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.