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Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem

Mossel, Elchanan and Tamuz, Omer (2012) Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem. Social Choice and Welfare, 39 (1). pp. 127-140. ISSN 0176-1714. doi:10.1007/s00355-011-0547-0. https://resolver.caltech.edu/CaltechAUTHORS:20161110-073042338

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Abstract

Arrow’s theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity), and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions, since non-strict preferences of the dictator are not necessarily followed. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow’s theorem, in the case of non-strict preferences, does not provide a complete characterization of all social welfare functions satisfying Transitivity, the Weak Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow’s theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow’s and Wilson’s result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Weak Pareto Principle). Additionally, we derive formulae for the number of functions satisfying these conditions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00355-011-0547-0DOIArticle
https://rdcu.be/bHRndPublisherFree ReadCube access
https://arxiv.org/abs/0910.2465arXivDiscussion Paper
ORCID:
AuthorORCID
Mossel, Elchanan0000-0001-7812-7886
Tamuz, Omer0000-0002-0111-0418
Additional Information:© 2011 Springer-Verlag. Received: 14 October 2009; Accepted: 22 March 2011; Published online: 2 April 2011. E. Mossel was supported by a Sloan fellowship in Mathematics, by BSF grant 2004105, NSF Career Award (DMS 054829), ONR award N00014-07-1-0506, and ISF grant 1300/08, and O. Tamuz was supported by ISF grant 1300/08.
Funders:
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)2004105
NSFDMS 054829
Office of Naval Research (ONR)N00014-07-1-0506
Israel Science Foundation1300/08
Subject Keywords:Equivalence Class; Complete Characterization; Social Welfare Function; Strict Preference; Social Alternative
Issue or Number:1
DOI:10.1007/s00355-011-0547-0
Record Number:CaltechAUTHORS:20161110-073042338
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161110-073042338
Official Citation:Mossel, E. & Tamuz, O. Soc Choice Welf (2012) 39: 127. https://doi.org/10.1007/s00355-011-0547-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71906
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:11 Nov 2016 02:12
Last Modified:11 Nov 2021 04:53

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