{"type":"ScholarlyArticle","title":"On the Axiomatic Foundations of Ranking Systems","authors":[{"name":"Alon Altman","slug":"alon-altman","given":"Alon","family":"Altman","affiliation":"Faculty of Industrial Engineering and Management Technion -Israel Institute of Technology Haifa 32000 Israel"},{"name":"Moshe Tennenholtz","slug":"moshe-tennenholtz","given":"Moshe","family":"Tennenholtz","affiliation":"Faculty of Industrial Engineering and Management Technion -Israel Institute of Technology Haifa 32000 Israel"}],"abstract":"Reasoning about agent preferences on a set of alternatives, and the aggregation of such preferences into some social ranking is a fundamental issue in reasoning about multi-agent systems. When the set of agents and the set of alternatives coincide, we get the ranking systems setting. A famous type of ranking systems are page ranking systems in the context of search engines. In this paper we present an extensive axiomatic study of ranking systems. In particular, we consider two fundamental axioms: Transitivity, and Ranked Independence of Irrelevant Alternatives. Surprisingly, we find that there is no general social ranking rule that satisfies both requirements. Furthermore, we show that our impossibility result holds under various restrictions on the class of ranking problems considered. Each of these axioms can be individually satisfied. Moreover, we show a complete axiomatization of approval voting using one of these axioms.","doi":null,"url":"https://ijcai.org/proceedings/2005/16","pdf":"https://ijcai.org/proceedings/2005/0016.pdf","markdown":"https://ijcai.org/proceedings/2005/16.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/16","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":16,"pages":{"first":917,"last":921},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[Altman and Tennenholtz, 2005] Alon Altman and Moshe Tennenholtz. Ranking systems: The pagerank axioms. 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