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Axioms for Defeat in Democratic Elections

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  • Wesley H. Holliday
  • Eric Pacuit

Abstract

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem and related impossibility results.

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  • Wesley H. Holliday & Eric Pacuit, 2020. "Axioms for Defeat in Democratic Elections," Papers 2008.08451, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2008.08451
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    Cited by:

    1. Harrison-Trainor, Matthew, 2022. "An analysis of random elections with large numbers of voters," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 68-84.

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