Arrow's Theorem in Spatial Environments

Lars Ehlers and Ton Storcken

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Keywords: Arrow's theorem; indendence of irrelevant alternatives (search for similar items in EconPapers)
JEL-codes: D70 D71 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2002
New Economics Papers: this item is included in nep-cdm
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:mtl:montde:2002-03

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