Arrow’s theorem through a fixpoint argument

Frank M.V. Feys, Helle Hvid Hansen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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 “stable points” (fixpoints) of a certain process.

Original languageEnglish
Title of host publicationProceedings Seventeenth Conference in Theoretical Aspects of Rationality and Knowledge, TARK 2019
EditorsLawrence S. Moss
PublisherElectronic Proceedings in Theoretical Computer Science (EPTCS)
Pages175-188
Number of pages14
DOIs
Publication statusPublished - 19-Jul-2019
Externally publishedYes
Event17th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2019 - Toulouse, France
Duration: 17-Jul-201919-Jul-2019

Publication series

NameElectronic Proceedings in Theoretical Computer Science, EPTCS
PublisherOPEN PUBL ASSOC
Volume297
ISSN (Print)2075-2180

Conference

Conference17th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2019
Country/TerritoryFrance
CityToulouse
Period17/07/201919/07/2019

Keywords

  • Arrow’s impossibility theorem
  • Banach’s fixpoint theorem
  • Dictatorship
  • Fixpoint
  • Force
  • Metric
  • Social choice theory
  • Voting

Cite this