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On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem
2006
Applied Mathematics and Computation
We will show that in the case where there are two individuals and three alternatives (or under the assumption of free-triple property) the Arrow impossibility theorem (Arrow (1963)) for social welfare functions that there exists no social welfare function which satisfies transitivity, Pareto principle, independence of irrelevant alternatives, and has no dictator is equivalent to the Brouwer fixed point theorem on a 2-dimensional ball (circle). Our study is an application of ideas by
doi:10.1016/j.amc.2005.02.054
fatcat:op6jqk6tgrhixprox727pke6lu