Multi-Winner Elections: Justified Representation, Strategyproofness, and Risk-Avoiding Truthfulness

2026-08-15

AI Summary

This study addresses the inherent tension between justified representation and strategy-proofness in approval-based multi-winner elections by integrating social choice theory with impossibility theorems. We first establish an impossibility result demonstrating that no mechanism can simultaneously satisfy strategy-proofness and Justified Representation (JR) under strategic voting. Furthermore, we introduce the RAT metric to quantify manipulation risk under partial information and evaluate the weak strategy-proofness of mainstream proportional rules. Our findings reveal a fundamental incompatibility between these properties and indicate that existing proportional methods exhibit poor RAT performance. Consequently, this work provides a novel theoretical foundation and quantitative framework for understanding strategic vulnerabilities in multi-winner electoral systems.

Abstract

We study approval-based multi-winner elections with justified representation (JR) when voters strategically report their ballots. We prove that there does not exist a strategy-proof mechanism that outputs JR committees, even when the mechanism can be randomized and only ex-ante strategy-proofness is required. The impossibility result holds for any fixed voter's monotone utility function. In addition, our impossibility result continues to hold for even more restrictive settings, such as the setting where we are allowed to select fewer than $k$ candidates, with only 4 candidates and 3 voters. Motivated by our negative results, we then ask for weaker strategy-proof guarantees under voters' partial information. We use the notion of RAT-degree proposed by Hartman, Segal-Halevi, and Tao (EC'25), the number of other voters whose information a manipulator must know before a safe and profitable deviation is possible. Standard proportional rules, such as greedy approval voting, proportional approval voting (PAV), and the method of equal shares (MES), have poor performances under the RAT-degree metric (with low RAT-degrees).

Problem

• Multi-Winner Elections
• Justified Representation
• Strategyproofness
• Risk-Avoiding Truthfulness
• Approval-Based Voting

Innovation

• Justified Representation
• Strategyproofness
• RAT-degree
• Approval-based Multi-winner Elections
• Impossibility Result