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

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  • Chris Dong

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.

Suggested Citation

  • Chris Dong, 2026. "Jointly Satisfying Pareto Optimality and Justified Representation is NP-Hard in Approval-Based Multiwinner Voting," Papers 2609.08357, arXiv.org.
    • Handle: RePEc:arx:papers:2609.08357
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    File URL: https://arxiv.org/pdf/2609.08357
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