{"type":"ScholarlyArticle","title":"Comparing Ways of Obtaining Candidate Orderings from Approval Ballots","authors":[{"name":"Théo Delemazure","slug":"theo-delemazure","given":"Théo","family":"Delemazure","affiliation":"CNRS , LAMSADE , Université Paris Dauphine -PSL"},{"name":"Chris Dong","slug":"chris-dong","given":"Chris","family":"Dong","affiliation":"Technical University of Munich"},{"name":"Dominik Peters","slug":"dominik-peters","given":"Dominik","family":"Peters","affiliation":"CNRS , LAMSADE , Université Paris Dauphine -PSL"},{"name":"Magdalena Tydrichova","slug":"magdalena-tydrichova","given":"Magdalena","family":"Tydrichova","affiliation":"CentraleSupélec , Paris Saclay University"}],"abstract":"To understand and summarize approval preferences and other binary evaluation data, it is useful to order the items on an axis which explains the data. In a political election using approval voting, this could be an ideological left-right axis such that each voter approves adjacent candidates, an analogue of single-peakedness. In a perfect axis, every approval set would be an interval, which is usually not possible, and so we need to choose an axis that gets closest to this ideal. The literature has developed algorithms for optimizing several objective functions (e.g., minimize the number of added approvals needed to get a perfect axis), but provides little help with choosing among different objectives. In this paper, we take a social choice approach and compare 5 different axis selection rules axiomatically, by studying the properties they satisfy. We establish some impossibility theorems, and characterize (within the class of scoring rules) the rule that chooses the axes that maximize the number of votes that form intervals, using the axioms of ballot monotonicity and resistance to cloning. Finally, we study the behavior of the rules on data from French election surveys, on the votes of justices of the US Supreme Court, and on synthetic data.","doi":"10.24963/ijcai.2024/305","url":"https://ijcai.org/proceedings/2024/305","pdf":"https://ijcai.org/proceedings/2024/0305.pdf","markdown":"https://ijcai.org/proceedings/2024/305.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/305","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":305,"pages":{"first":2757,"last":2765},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice"],"videos":[],"references":[{"position":1,"raw":"[Baujard and Lebon, 2022] Antoinette Baujard and Isabelle Lebon. 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