{"type":"ScholarlyArticle","title":"Preferences Single-Peaked on a Tree: Sampling and Tree Recognition","authors":[{"name":"Jakub Sliwinski","slug":"jakub-sliwinski","given":"Jakub","family":"Sliwinski","affiliation":"ETH Zurich"},{"name":"Edith Elkind","slug":"edith-elkind","given":"Edith","family":"Elkind","affiliation":"University of Oxford"}],"abstract":"In voting theory, impossibility results and computational hardness results are often circumvented by recognising that voters' preferences are not arbitrary, but lie within a restricted domain. Uncovering the structure of the underlying domain often provides useful insights about the nature of the alternative space, and may be helpful in identifying a collective choice. Preferences single-peaked on a tree are an example of a relatively broad domain that nonetheless exhibits several desirable properties. We consider the setting where voters' preferences are independently sampled from rankings that are single-peaked on a given tree, and study the problem of reliably identifying the tree that generated the observed votes. We test our algorithm empirically; to this end, we develop an algorithm to uniformly sample preferences that are single-peaked on a given tree.","doi":"10.24963/ijcai.2019/82","url":"https://ijcai.org/proceedings/2019/82","pdf":"https://ijcai.org/proceedings/2019/0082.pdf","markdown":"https://ijcai.org/proceedings/2019/82.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/82","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":82,"pages":{"first":580,"last":586},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[],"references":[{"position":1,"raw":"Arrow, 1951","title":null,"authors":"Arrow","year":"1951","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"Kenneth J. 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