Researchers have explored automated reasoning to narrow the gap between theoretical bounds for Condorcet winning sets in elections. While it's known that a committee of size 5 always exists, and a lower bound suggests 3 candidates might be needed, this work investigates if 4 are sufficient. Using a mixed-integer linear program to search for counter-examples, the team found no instances requiring more than 3 candidates. This empirical evidence supports a conjecture that a winning set of size 4 always exists, offering a new analytical path through linear programming duality. AI
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RANK_REASON Academic paper presenting new theoretical bounds and empirical evidence for Condorcet winning sets in elections.