@inproceedings{2ef242d89bfa412ea51f7ee0c23f97b0,

title = "Arrow{\textquoteright}s theorem through a fixpoint argument",

abstract = "We present a proof of Arrow{\textquoteright}s theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach{\textquoteright}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.",

keywords = "Arrow{\textquoteright}s impossibility theorem, Banach{\textquoteright}s fixpoint theorem, Dictatorship, Fixpoint, Force, Metric, Social choice theory, Voting",

author = "Feys, {Frank M.V.} and Hansen, {Helle Hvid}",

note = "Funding Information: We would like to thank Thomas Santoli for pointing out in a discussion that the permutation structure gives rise to a group action, which ultimately led to Proposition 3.13, and Ronald de Wolf for inspiring us to formalize and study the notion of force. Publisher Copyright: {\textcopyright} Frank M. V. Feys & Helle Hvid Hansen.; 17th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2019 ; Conference date: 17-07-2019 Through 19-07-2019",

year = "2019",

month = jul,

day = "19",

doi = "10.4204/EPTCS.297.12",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science, EPTCS",

publisher = "Electronic Proceedings in Theoretical Computer Science (EPTCS)",

pages = "175--188",

editor = "Moss, {Lawrence S.}",

booktitle = "Proceedings Seventeenth Conference in Theoretical Aspects of Rationality and Knowledge, TARK 2019",

}