The probability of violating Arrow’s conditions

Keith L. Dougherty and Jac Heckelman

European Journal of Political Economy, 2020, vol. 65, issue C

Abstract: Arrow’s impossibility theorem shows that all preference aggregation rules (PARs) must violate a specific set of normative conditions (transitivity, Pareto, IIA, nondictatorship) over an unrestricted domain of preference profiles. However, the theorem does not address which PARs are more likely to violate those conditions across preference profiles. We compare the probabilities that thirteen PARs (anti-plurality, Hare, Nanson, plurality, plurality runoff, Simpson–Kramer, Baldwin, Borda, Coombs, Copeland, Dowdall, pairwise majority, and ranked pairs) violate Arrow’s conditions. We prove that Baldwin, Borda, Coombs, Copeland, Dowdall, and ranked pairs are less likely to violate IIA than the first six PARs, and they are less likely to violate Arrow’s conditions jointly. In contrast, pairwise majority never violates IIA but can violate transitivity. Simulations with three alternatives reveal that among the PARs studied, pairwise majority is the most likely to satisfy Arrow’s conditions jointly. Our results suggest pairwise majority violates transitivity with a small probability, while the other PARs violate IIA with much larger probabilities.

Keywords: Arrow impossibility theorem; Social choice; Transitivity; Pareto; Independence of irrelevant alternatives (search for similar items in EconPapers)
JEL-codes: D71 H00 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:poleco:v:65:y:2020:i:c:s0176268020300847

DOI: 10.1016/j.ejpoleco.2020.101936

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