{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/new-record-breaking-condorcet-domains-on-10","title":"A heuristic search algorithm for discovering large Condorcet domains","arxiv_id":"2303.06524","date":"2023-03-12","proceeding":null,"authors":["Bei Zhou","Søren Riis"],"abstract":"The study of large Condorcet domains (CD) has been a significant area of interest in voting theory. In this paper, our goal is to search for large CDs that are hitherto unknown. With a straightforward combinatorial definition, searching for large CDs is naturally suited for algorithmic optimisations. For each value of n>2, one can ask for the size of the largest CD, thus finding the largest CDs provides an important benchmark for heuristic-based combinatorial optimisation algorithms. Despite extensive research over the past three decades, the CD sizes identified in 1996 remain the best known for many values of n. When n>8, conducting an exhaustive search becomes computationally unfeasible, thereby prompting the use of heuristic methods. To address this, we developed a novel heuristic search algorithm in which a specially designed heuristic function, backed by a lookup database, directs the search towards promising branches in the search tree. Our algorithm found new large CDs of size 1082 (surpassing the previous record of 1069) for n=10, and 2349 (improving the previous 2324) for n=11. Notably, these newly discovered CDs exhibit characteristics distinct from those of known CDs.","url_abs":"https://arxiv.org/abs/2303.06524v4","url_pdf":"https://arxiv.org/pdf/2303.06524v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"new-record-breaking-condorcet-domains-on-10","repo_url":"https://github.com/sagebei/cdl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}