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A number of rules for resolving majority cycles in elections have beenproposed in the literature. Recently, Holliday and Pacuit (Journal ofTheoretical Politics 33 (2021) 475-524) axiomatically characterized the classof rules refined by one such cycle-resolving rule, dubbed Split Cycle: in eachmajority cycle, discard the majority preferences with the smallest majoritymargin. They showed that any rule satisfying five standard axioms, plus aweakening of Arrow's Independence of Irrelevant Alternatives (IIA) calledCoherent IIA, is refined by Split Cycle. In this paper, we go further and showthat Split Cycle is the only rule satisfying the axioms of Holliday and Pacuittogether with two additional axioms: Coherent Defeat and Positive Involvementin Defeat. Coherent Defeat states that any majority preference not occurring ina cycle is retained, while Positive Involvement in Defeat is closely related tothe well-known axiom of Positive Involvement (as in J. P\'{e}rez, Social Choiceand Welfare 18 (2001) 601-616). We characterize Split Cycle not only as acollective choice rule but also as a social choice correspondence, over bothprofiles of linear ballots and profiles of ballots allowing ties.

An Axiomatic Characterization of Split Cycle