The connection between Arrow theorem and Sperner lemma
Combinatorics
2022-12-26 v1 Theoretical Economics
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.
Cite
@article{arxiv.2212.12251,
title = {The connection between Arrow theorem and Sperner lemma},
author = {Nikita Miku},
journal= {arXiv preprint arXiv:2212.12251},
year = {2022}
}