{"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/properties-of-position-matrices-and-their","title":"Properties of Position Matrices and Their Elections","arxiv_id":"2303.02538","date":"2023-03-05","proceeding":null,"authors":["Niclas Boehmer","Jin-Yi Cai","Piotr Faliszewski","Austen Z. Fan","Łukasz Janeczko","Andrzej Kaczmarczyk","Tomasz Wąs"],"abstract":"We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given position matrix is #P-complete. Consequently, sampling such elections uniformly at random seems challenging and we propose a simpler algorithm, without hard guarantees. Next, we consider the problem of testing if a given matrix can be implemented by an election with a certain structure (such as single-peakedness or group-separability). Finally, we consider the problem of checking if a given position matrix can be implemented by an election with a Condorcet winner. We complement our theoretical findings with experiments.","url_abs":"https://arxiv.org/abs/2303.02538v3","url_pdf":"https://arxiv.org/pdf/2303.02538v3.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":"properties-of-position-matrices-and-their","repo_url":"https://github.com/project-pragma/position-matrices-aaai-2023","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":"https://syntology.ai/paper/2303.02538","atlas_url":"https://app.syntology.ai/?focus=2303.02538","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}