{"type":"ScholarlyArticle","title":"An Ordinal Banzhaf Index for Social Ranking","authors":[{"name":"Hossein Khani","slug":"hossein-khani","given":"Hossein","family":"Khani","affiliation":"Université Paris-Dauphine , PSL Research University , CNRS , LAMSADE , Place du Maréchal de Lattre de Tassigny , F-75775 Paris cedex 16 , France"},{"name":"Stefano Moretti","slug":"stefano-moretti","given":"Stefano","family":"Moretti","affiliation":"Université Paris-Dauphine , PSL Research University , CNRS , LAMSADE , Place du Maréchal de Lattre de Tassigny , F-75775 Paris cedex 16 , France"},{"name":"Meltem Öztürk","slug":"meltem-ozturk","given":"Meltem","family":"Öztürk","affiliation":"Université Paris-Dauphine , PSL Research University , CNRS , LAMSADE , Place du Maréchal de Lattre de Tassigny , F-75775 Paris cedex 16 , France"}],"abstract":"We introduce a new method to rank single elements given an order over their sets. For this purpose, we extend the game theoretic notion of marginal contribution and of Banzhaf index to our ordinal framework. Furthermore, we characterize the resulting ordinal Banzhaf solution by means of a set of properties inspired from those used to axiomatically characterize another solution from the literature: the ceteris paribus majority. Finally, we show that the computational procedure for these two social ranking solutions boils down to a weighted combination of comparisons over the same subsets of elements.","doi":"10.24963/ijcai.2019/54","url":"https://ijcai.org/proceedings/2019/54","pdf":"https://ijcai.org/proceedings/2019/0054.pdf","markdown":"https://ijcai.org/proceedings/2019/54.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/54","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":54,"pages":{"first":378,"last":384},"keywords":["Agent-based and Multi-agent Systems: Cooperative Games","Agent-based and Multi-agent Systems: Voting","Knowledge Representation and Reasoning: Knowledge Representation and  Game Theory ; Social Choice"],"videos":[],"references":[{"position":1,"raw":"[Banzhaf III, 1964] John F Banzhaf III. 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