On fixed point theorems and social choice paradoxes
type: Item
instance of: scholarly article
title: On fixed point theorems and social choice paradoxes
zbMATH Open document ID: 0693.90008
DOI: 10.1016/0165-1765(79)90009-0
author: Graciela Chichilnisky
published in: Economics Letters
publication date: 1979-01-01T00:00:00Z
review text: In the case of two voters and two-dimensional choice spaces the author shows that the nonexistence of a continuous and anonymous rule that satisfies unanimity is equivalent to a fixed point problem. Specifically, the main result is that the existence of such a choice rule is equivalent to the existence of a continuous map from the closed unit disk of \({\mathbb{R}}^ 2\) into itslf without fixed points. The author also indicates how the result can be extended to higher-dimensional choice spaces and any finite number of voters.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 4135654
zbMATH Keywords: fixed point theorems
zbMATH Keywords: social choice paradoxes
zbMATH Keywords: impossibility theorem
zbMATH Keywords: nonexistence
zbMATH Keywords: continuous and anonymous rule
zbMATH Keywords: unanimity
MaRDI profile type: Publication
full work available at URL: 0165-1765(79)90009-0
OpenAlex ID: W3123829701
cites work: Social choice and individual values
cites work: Social choice and the topology of spaces of preferences
cites work: Q5510566
cites work: Q5522742
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description: scientific article; zbMATH DE number 4135654