Arrow’s Theorem Through a Fixpoint Argument

Frank Feys; Helle Hansen

doi:10.4204/EPTCS.297.12

Arrow’s Theorem Through a Fixpoint Argument

Frank Feys, Helle Hansen

Energy and Industry

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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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 fixpoints of a certain process.

Original language	English
Title of host publication	Proceedings TARK 2019
Publisher	Electronic Proceedings in Theoretical Computer Science
Pages	175-188
Number of pages	14
Volume	297
DOIs	https://doi.org/10.4204/EPTCS.297.12
Publication status	Published - 2019
Event	Theoretical Aspects of Rationality and Knowledge - Toulouse, France Duration: 17 Jul 2019 → 19 Jul 2019 Conference number: 17

Publication series

Name	Electronic Proceedings in Theoretical Computer Science, EPTCS
Publisher	Open Publishing Association
ISSN (Print)	2075-2180

Conference

Conference	Theoretical Aspects of Rationality and Knowledge
Abbreviated title	TARK
Country/Territory	France
City	Toulouse
Period	17/07/19 → 19/07/19

Keywords

Social choice theory
voting
Arrow’s impossibility theorem
Banach’s fixpoint theorem
dictatorship
force
fixpoint
metric

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10.4204/EPTCS.297.12

1907.10381v1Final published version, 213 KBLicence: CC BY

Cite this

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title = "Arrow{\textquoteright}s Theorem Through a Fixpoint Argument",

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 fixpoints of a certain process. ",

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author = "Frank Feys and Helle Hansen",

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doi = "10.4204/EPTCS.297.12",

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volume = "297",

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

publisher = "Electronic Proceedings in Theoretical Computer Science",

pages = "175--188",

booktitle = "Proceedings TARK 2019",

note = "Theoretical Aspects of Rationality and Knowledge, TARK ; Conference date: 17-07-2019 Through 19-07-2019",

}

Arrow’s Theorem Through a Fixpoint Argument. / Feys, Frank; Hansen, Helle.
Proceedings TARK 2019. Vol. 297 Electronic Proceedings in Theoretical Computer Science, 2019. p. 175-188 (Electronic Proceedings in Theoretical Computer Science, EPTCS).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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KW - force

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Y2 - 17 July 2019 through 19 July 2019

ER -

Arrow’s Theorem Through a Fixpoint Argument

Abstract

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Keywords

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