{"type":"ScholarlyArticle","title":"On the Complexity of Winner Verification and Candidate Winner for Multiwinner Voting Rules","authors":[{"name":"Chinmay Sonar","slug":"chinmay-sonar","given":"Chinmay","family":"Sonar","affiliation":"University of California , Santa Barbara"},{"name":"Palash Dey","slug":"palash-dey","given":"Palash","family":"Dey","affiliation":"Indian Institute of Technology Kharagpur"},{"name":"Neeldhara Misra","slug":"neeldhara-misra","given":"Neeldhara","family":"Misra","affiliation":"Indian Institute of Technology Gandhinagar"}],"abstract":"The Chamberlin-Courant and Monroe rules are fundamental and well-studied rules in the literature of multi-winner elections. The problem of determining if there exists a committee of size k that has a Chamberlin-Courant (respectively, Monroe) dissatisfaction score of at most r is known to be NP-complete. We consider the following natural problems in this setting: a) given a committee S of size k as input, is it an optimal k-sized committee?, and b) given a candidate c and a committee size k, does there exist an optimal k-sized committee that contains c? In this work, we resolve the complexity of both problems for the Chamberlin-Courant and Monroe voting rules in the settings of rankings as well as approval ballots. We show that verifying if a given committee is optimal is coNP-complete whilst the latter problem is complete for Theta_2^P. Our contribution fills an essential gap in the literature for these important multi-winner rules.","doi":"10.24963/ijcai.2020/13","url":"https://ijcai.org/proceedings/2020/13","pdf":"https://ijcai.org/proceedings/2020/0013.pdf","markdown":"https://ijcai.org/proceedings/2020/13.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/13","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":13,"pages":{"first":89,"last":95},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25221/file_25221.m3u8","length_sec":274,"provider":"hls"}],"references":[{"position":1,"raw":"[Bartholdi et al., 1989] John Bartholdi, Craig A Tovey, and Michael A Trick. 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