On the Edge of Core (Non-)Emptiness: An Automated Reasoning Approach to Approval-Based Multi-Winner Voting

Ratip Emin Berker, Emanuel Tewolde, Vincent Conitzer, Mingyu Guo, Marijn Heule, Lirong Xia

Keywords: multi-winner voting, core stability, automated reasoning

TL;DR: We develop a mixed‐integer linear programming framework with which we prove the existence of core‐stable committees in special cases of approval-based multi-winner voting, and investigate the connection of core stability to other axioms.

Abstract: Core stability is a natural and well-studied notion for group fairness in multi-winner voting, where the task is to select a committee from a pool of candidates. We study the setting where voters either approve or disapprove of each candidate; here, it remains a major open problem whether a core-stable committee always exists. In this work, we develop an approach based on mixed-integer linear programming for deciding whether and when core-stable committees are guaranteed to exist. In contrast to SAT-based approaches popular in computational social choice, our method can produce proofs for a specific number of candidates _independent_ of the number of voters. In addition to these computational gains, our program lends itself to a novel duality-based reformulation of the core stability problem, from which we obtain new existence results in special cases. Further, we use our framework to reveal previously unknown relationships between core stability and other desirable properties, such as notions of priceability.

Track: Long Paper

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Submission Number: 72