On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders

Yasuhito Tanaka

Journal of Mathematical Economics, 2009, vol. 45, issue 3-4, 241-249

Abstract: We will show that in the case where there are two individuals and three alternatives (or under the assumption of the free-triple property), and individual preferences are weak orders (which may include indifference relations), the Arrow impossibility theorem [Arrow, K.J., 1963. Social Choice and Individual Values, second ed. Yale University Press] that there exists no binary social choice rule which satisfies the conditions of transitivity, Pareto principle, independence of irrelevant alternatives, and non-existence of dictator is equivalent to the Brouwer fixed point theorem on a 2-dimensional ball (circle). Our study is an application of ideas by Chichilnisky [Chichilnisky, G., 1979. On fixed points and social choice paradoxes. Economics Letters 3, 347-351] to a discrete social choice problem, and also it is in line with the work by Baryshnikov [Baryshnikov, Y., 1993. Unifying impossibility theorems: a topological approach. Advances in Applied Mathematics 14, 404-415].

Keywords: The; Arrow; impossibility; theorem; Weak; orders; Homology; groups; of; simplicial; complexes; The; Brouwer; fixed; point; theorem (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:45:y:2009:i:3-4:p:241-249

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