{"type":"ScholarlyArticle","title":"A Savage-style Utility Theory for Belief Functions","authors":[{"name":"Chunlai Zhou","slug":"chunlai-zhou","given":"Chunlai","family":"Zhou","affiliation":"Computer Science Department , Renmin University of China , Beijing , CHINA"},{"name":"Biao Qin","slug":"biao-qin","given":"Biao","family":"Qin","affiliation":"Computer Science Department , Renmin University of China , Beijing , CHINA"},{"name":"Xiaoyong Du","slug":"xiaoyong-du","given":"Xiaoyong","family":"Du","affiliation":"Computer Science Department , Renmin University of China , Beijing , CHINA"}],"abstract":"In this paper, we provide an axiomatic justification for decision making with belief functions by studying the belief-function counterpart of Savage's Theorem where the state space is finite and the consequence set is a continuum [l, M] (l<M). We propose six axioms for a preference relation over acts, and then show that this axiomatization admits a definition of qualitative belief functions comparing preferences over events that guarantees the existence of a belief function on the state space. The key axioms are uniformity and an analogue of the independence axiom. The uniformity axiom is used to ensure that all acts with the same maximal and minimal consequences must be equivalent. And our independence axiom shows the existence of a utility function and  implies the uniqueness of the belief function on the state space.  Moreover, we prove  without the independence axiom the neutrality theorem that two acts are indifferent whenever they generate the same belief functions over consequences. At the end of the paper, we compare our approach with other related decision theories for belief functions.","doi":"10.24963/ijcai.2018/712","url":"https://ijcai.org/proceedings/2018/712","pdf":"https://ijcai.org/proceedings/2018/0712.pdf","markdown":"https://ijcai.org/proceedings/2018/712.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/712","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":"Uncertainty in AI","track":"Main track","number":712,"pages":{"first":5135,"last":5141},"keywords":["Uncertainty in AI: Decision;Utility Theory","Uncertainty in AI: Uncertainty in AI"],"videos":[],"references":[{"position":1,"raw":"[Arrow and Hurwicz, 1972] Kenneth Arrow and Leonid. 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