Axioms for defeat in democratic elections. (October 2021)

• Record Type: Journal Article
• Authors: Holliday, Wesley H.; Pacuit, Eric
• Is Part Of: Journal of theoretical politics. Volume 33:Number 4(2021)
• Page Start: 475
• Page End: 524
• Publication Date: 2021-10
• Subjects: Arrow's impossibility theorem -- independence of irrelevant alternatives -- majority cycle -- spoiler effect -- voting theory; Political science -- Periodicals; 320
• DOI: 10.1177/09516298211043236
• Languages: English
• ISSNs: 0951-6298

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.