Human-AI Collaboration Settles Major Open Problem in Multi-Winner Voting Theory
xuanalogue · x · 2026-09-21
Another problem from FrontierMath: Open Problems has been solved. In approval-based multi-winner elections, researchers asked whether a committee satisfying "core stability" — a formalization of proportional representation based on the core from cooperative game theory — always exists.
- The answer is yes. Becker, Greger, and Dominik Peters derived the proof in an interactive session with GPT-6 Astra; Peters originally proposed the problem for the benchmark
- The proof introduces a new voting rule optimizing an entropy-like objective dubbed "harmonic entropy"; all local optima lie in the core, implying a core committee can be found in polynomial time
- The authors stress the work blended existing ideas in the subfield in a novel way and required human domain expertise
The 20-page paper is on arXiv (2609.11912), submitted Sep 10, 2026.
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