Jointly Satisfying Pareto Optimality and Justified Representation is NP-Hard in Approval-Based Multiwinner Voting

2026-09-08

AI Summary

研究证明在基于批准的多胜者投票中，同时满足正当代表性和帕累托最优性的委员会计算问题是NP难的。

Abstract

An open problem in approval-based multiwinner voting concerns whether we can efficiently compute committees that satisfy both justified representation and Pareto optimality. We answer this question negatively by proving that, on the domain of all profiles, outputting a committee satisfying both axioms is NP-hard. An initial proof was found by ChatGPT Astra. This was then verified and rewritten by the author.

Problem

• approval-based multiwinner voting
• justified representation
• Pareto optimality
• NP-hard

Innovation

• Pareto Optimality
• Justified Representation
• Approval-Based Voting
• NP-Hard