Core-stable committees always exist for approval-based elections with up to 8 seats or up to 15 candidates, proved via Proportional Approval Voting and computer-verified linear programming certificates.
Mathematical Programming (2022)
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The Core of Approval-Based Committee Elections with Few Seats
Core-stable committees always exist for approval-based elections with up to 8 seats or up to 15 candidates, proved via Proportional Approval Voting and computer-verified linear programming certificates.