English

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}
}
R2 v1 2026-06-28T07:50:22.771Z