Arrow's impossibility theorem: Two simple single-profile versions

Allan M. Feldman () and Roberto Serrano
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Allan M. Feldman: Brown University

No 2007-07, Working Papers from Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales

Abstract: In this short paper we provide two simple new versions of Arrow's impossibility theorem, in a world with only one preference profile. Both versions are extremely transparent. The first version assumes a two-agent society; the second version, which is similar to a theorem of Pollak, assumes two or more agents. Both of our theorems rely on diversity of preferences axioms, and we explore alternative notions of diversity at length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to show the logical independence of the axioms, and to illustrate our points.

Keywords: Arrow's theorem; single-profile (search for similar items in EconPapers)
JEL-codes: D60 D70 D71 (search for similar items in EconPapers)
Date: 2007-02-28
New Economics Papers: this item is included in nep-cdm
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Published in Harvard College Mathematics Review 2(2), December 2008: 46-57

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