On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem (forthcoming in ``Applied Mathematics and Computation''(Elsevier))
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 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).
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