Arrow's Theorem Through a Fixpoint Argument

07/22/2019

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by   Frank M. V. Feys, et al.

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We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our approach shows that dictatorships can be seen as fixpoints of a certain process.