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Recently, Holliday and Pacuit (J Theor Polit 33:475\u2013524, 2021) axiomatically characterized the class of rules refined by one such cycle-resolving rule, dubbed Split\u00a0Cycle: in each majority cycle, discard the majority preferences with the smallest majority margin. They showed that any rule satisfying five standard axioms plus a weakening of Arrow\u2019s Independence of Irrelevant Alternatives\u00a0(IIA), called Coherent IIA, is refined by Split Cycle. In this paper, we go further and show that Split Cycle is the only rule satisfying the axioms of Holliday and Pacuit together with two additional axioms, which characterize the class of rules that refine Split Cycle: Coherent Defeat and Positive Involvement in Defeat. Coherent Defeat states that any majority preference not occurring in a cycle is retained, while Positive Involvement in Defeat is closely related to the well-known axiom of Positive Involvement (as in J P\u00e9rez Soc Choice Welf 18:601\u2013616, 2001). We characterize Split\u00a0Cycle not only as a collective choice rule but also as a social choice correspondence, over both profiles of linear ballots and profiles of ballots allowing ties.<\/jats:p>","DOI":"10.1007\/s00355-024-01539-w","type":"journal-article","created":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T15:03:14Z","timestamp":1725634994000},"page":"557-601","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An axiomatic characterization of Split Cycle"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0813-3986","authenticated-orcid":false,"given":"Yifeng","family":"Ding","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6054-9052","authenticated-orcid":false,"given":"Wesley H.","family":"Holliday","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0751-9011","authenticated-orcid":false,"given":"Eric","family":"Pacuit","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,6]]},"reference":[{"key":"1539_CR1","unstructured":"Arrow KJ (1963) Arrow. 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