New Record-Breaking Condorcet Domains on 10 and 11 Alternatives

We report on discovering new record-breaking Condorcet domains on $n=10$ and n=11 alternatives, challenging long-standing voting theory results. Our work presents new records with sizes of 1082 (previous record 1069) for n=10 and 2349 (previous record 2324) for $n=11$, which appear sporadic and do not fit into the existing alternating schema discovered in 1996. While the method used to discover these domains was inspired by the application of value functions in reinforcement learning, a subcategory of artificial intelligence, the current version of the method is somewhat ad-hoc and unstable. Therefore, we will not expound on the search method in this paper. Instead, we outline the key components that contribute to the success of our approach. We will also discuss the theoretical implications of our findings and explore the structure of the new Condorcet domains, raising several open questions related to them. Our results contribute to the ongoing investigation of Condorcet domains and their mathematical properties, potentially demonstrating the power of artificial intelligence-inspired problem-solving methods in advancing mathematical research.