{"type":"ScholarlyArticle","title":"Multiwinner Elections under Minimax Chamberlin-Courant Rule in Euclidean Space","authors":[{"name":"Chinmay Sonar","slug":"chinmay-sonar","given":"Chinmay","family":"Sonar","affiliation":"University of California , Santa Barbara"},{"name":"Subhash Suri","slug":"subhash-suri","given":"Subhash","family":"Suri","affiliation":"University of California , Santa Barbara"},{"name":"Jie Xue","slug":"jie-xue","given":"Jie","family":"Xue","affiliation":"New York University , Shanghai"}],"abstract":"We consider multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule.\r\nIn this setting, voters and candidates are embedded in a d-dimensional Euclidean space,\r\nand the goal is to choose a committee of k candidates so that the rank of any voter's\r\nmost preferred candidate in the committee is minimized. (The problem is also equivalent to the \r\nordinal version of the classical k-center problem.) \r\nWe show that the problem is NP-hard in any dimension d >= 2, and also provably hard to approximate.\r\nOur main results are three polynomial-time approximation schemes, each of which finds a committee \r\nwith provably good minimax score. In all cases, we show that our approximation bounds are tight or close to tight.\r\nWe mainly focus on the 1-Borda rule but some of our results also hold for the more general r-Borda.","doi":"10.24963/ijcai.2022/68","url":"https://ijcai.org/proceedings/2022/68","pdf":"https://ijcai.org/proceedings/2022/0068.pdf","markdown":"https://ijcai.org/proceedings/2022/68.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/68","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":68,"pages":{"first":475,"last":481},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986536","length_sec":91,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984679","length_sec":336,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Aziz et al., 2018] Haris Aziz, Piotr Faliszewski, Bernard Grofman, Arkadii Slinko, and Nimrod Talmon. 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