Arrow's Theorem in Spatial Environments

Lars Ehlers and T. Storcken

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

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; independence of irrelevant alternatives (search for similar items in EconPapers)
JEL-codes: D71 D70 (search for similar items in EconPapers)
Date: Written 2002
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Related works:
Working Paper: Arrow's Theorem in Spatial Environments (2002)
Working Paper: Arrow's Theorem in Spatial Environments (2001)
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