Understanding the Impact of Proportionality in Approval-Based Multiwinner Elections

2025-11-12

AI Summary

This study investigates the practical restrictiveness of proportionality principles on feasible committees and candidate sets in approval-based multiwinner elections. Methodologically, we formalize multiple proportionality axioms and conduct a joint analysis combining computational complexity theory with large-scale experiments on both real-world and synthetic datasets. Our key contribution is the introduction of the “proportionality criticality” metric—a novel measure quantifying the necessity of individual candidates for satisfying proportionality—thereby extending beyond traditional approval-score-based evaluation. Empirical results reveal unexpectedly strong constraints in real elections, demonstrating that proportionality does not impose uniform restrictions; rather, its effective restrictiveness critically depends on the structure of voter approval patterns. The proportionality criticality metric reliably identifies pivotal candidates, offering actionable, empirically grounded insights for voting rule design and election auditing.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Constraint Satisfaction and Optimization: Satisfiability
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the computational complexity of several natural problems related to the behavior of proportionality axioms, and (ii) conducting an extensive experimental study on both real-world and synthetic elections. Our findings reveal substantial variation in the restrictiveness of proportionality across instances, including previously unobserved high levels of restrictiveness in some real-world cases. We also introduce and evaluate new measures for quantifying a candidate's importance for achieving proportional outcomes, which differ clearly from assessing candidate strength by approval score.

Problem

• Analyzing computational complexity of proportionality axioms in multiwinner elections
• Measuring real-world restrictiveness of proportional representation rules
• Introducing new metrics for candidate importance in achieving proportionality

Innovation

• Analyzing computational complexity of proportionality axioms
• Conducting experiments on real-world and synthetic elections
• Introducing new measures for candidate importance in proportionality