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arXiv · 2609.11912

Existence of the Core in Approval-Based Committee Elections

Patrick Becker·Matthias Greger·Dominik Peters
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Abstract

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

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Patrick Becker, Matthias Greger, Dominik Peters. 2026-09-10. Existence of the Core in Approval-Based Committee Elections. https://arxiv.org/abs/2609.11912

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