Allocation Proportionality of OWA--Based Committee Scoring Rules

2026-02-10

AI Summary

This work addresses the lack of a consistent measure for proportionality in multi-winner voting that aligns with traditional apportionment principles. It introduces the concept of “allocation proportionality” and, for the first time, establishes a quantitative metric tailored to party-based electoral frameworks, thereby bridging the theoretical gap between apportionment-based and committee-based notions of proportionality. By leveraging Ordered Weighted Averaging (OWA) operators, the study constructs committee scoring rules integrated with a party affiliation model to systematically evaluate the deviation of existing rules—such as SNTV, k-Borda, and Chamberlin–Courant—from ideal allocation proportionality. Experimental results quantitatively reveal performance disparities among current rules in achieving proportional representation, offering a principled foundation for the design and selection of multi-winner voting mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web measurements

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.

Problem

• proportionality
• multiwinner voting
• apportionment
• allocation proportionality
• party elections

Innovation

• allocation proportionality
• OWA-based committee scoring rules
• multiwinner voting
• proportionality measure
• party elections