{"type":"ScholarlyArticle","title":"Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?","authors":[{"name":"Jan Maly","slug":"jan-maly","given":"Jan","family":"Maly","affiliation":"TU Wien , Austria"},{"name":"Miroslaw Truszczynski","slug":"miroslaw-truszczynski","given":"Miroslaw","family":"Truszczynski","affiliation":"University of Kentucky , USA"},{"name":"Stefan Woltran","slug":"stefan-woltran","given":"Stefan","family":"Woltran","affiliation":"TU Wien , Austria"}],"abstract":"Lifting a preference order on elements of some universe to a preference order on subsets of this universe is often guided by postulated properties the lifted order should have. Well-known impossibility results pose severe limits on when such liftings exist if all non-empty subsets of the universe are to be ordered. The extent to which these negative results carry over to other families of sets is not known. In this paper, we consider families of sets that induce connected subgraphs in graphs. For such families, common in applications, we study whether lifted orders satisfying the well-studied axioms of dominance and (strict) independence exist for every or, in another setting, only for some underlying order on elements (strong and weak orderability). We characterize families that are strongly and weakly orderable under dominance and strict independence, and obtain a tight bound on the class of families that are strongly orderable under dominance and independence.","doi":"10.24963/ijcai.2018/60","url":"https://ijcai.org/proceedings/2018/60","pdf":"https://ijcai.org/proceedings/2018/0060.pdf","markdown":"https://ijcai.org/proceedings/2018/60.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/60","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":60,"pages":{"first":433,"last":439},"keywords":["Knowledge Representation and Reasoning: Preference Modelling and Preference-Based Reasoning","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[],"references":[{"position":1,"raw":"[Barberà and Pattanaik, 1984] Salvador Barberà and Pras- anta K. 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