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arXiv · 2212.12251

The connection between Arrow theorem and Sperner lemma

Nikita Miku
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Abstract

It is well known that Sperner lemma is equivalent to Brouwer fixed-point theorem. Tanaka [12] proved that Brouwer theorem is equivalent to Arrow theorem, hence Arrow theorem is equivalent to Sperner lemma. In this paper we will prove this result directly. Moreover, we describe a number of other statements equivalent to Arrow theorem.

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Nikita Miku. 2022-12-23. The connection between Arrow theorem and Sperner lemma. https://arxiv.org/abs/2212.12251

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