{"type":"ScholarlyArticle","title":"Explaining Preferences by Multiple Patterns in Voters’ Behavior","authors":[{"name":"Sonja Kraiczy","slug":"sonja-kraiczy","given":"Sonja","family":"Kraiczy","affiliation":"Department of Computer Science , University of Oxford"},{"name":"Edith Elkind","slug":"edith-elkind","given":"Edith","family":"Elkind","affiliation":"Department of Computer Science , University of Oxford"}],"abstract":"In some preference aggregation scenarios, voters' preferences are highly structured: e.g., the set of candidates may have one-dimensional structure (so that voters' preferences are single-peaked) or be described by a binary decision tree (so that voters' preferences are group-separable). However, sometimes a single axis or a decision tree is insufficient to capture the voters' preferences; rather, there is a small number K of axes or decision trees such that each vote in the profile is consistent with one of these axes (resp., trees). In this work, we study the complexity of deciding whether voters' preferences can be explained in this manner. For K=2, we use the technique developed by Yang [2020, https://doi.org/10.3233/FAIA200099] in the context of single-peaked preferences to obtain a polynomial-time algorithm for several domains: value-restricted preferences, group-separable preferences, and a natural subdomain of group-separable preferences, namely, caterpillar group-separable preferences. For K > 2, the problem is known to be hard for single-peaked preferences; we establish that it is also hard for value-restricted and group-separable preferences. Our positive results for K=2 make use of forbidden minor characterizations of the respective domains; in particular, we establish that the domain of caterpillar group-separable preferences admits a forbidden minor characterization.","doi":"10.24963/ijcai.2022/53","url":"https://ijcai.org/proceedings/2022/53","pdf":"https://ijcai.org/proceedings/2022/0053.pdf","markdown":"https://ijcai.org/proceedings/2022/53.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/53","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":53,"pages":{"first":370,"last":376},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986949","length_sec":86,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985092","length_sec":357,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Ballester and Haeringer, 2011] Miguel A Ballester and Guillaume Haeringer. 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