Topological social choice
type: Item
instance of: scholarly article
title: Topological social choice
zbMATH Open document ID: 0998.91011
DOI: 10.1016/S0165-4896(99)00036-0
author: Luc Lauwers
published in: Mathematical Social Sciences
publication date: 2002-11-24T00:00:00Z
review text: The author surveys the main results on topological social choice theory as initiated by Chichilnisky. In topological social choice, individual preferences are assumed to be smooth over some Euclidean space. The main result in the field is that under suitable conditions, a continuous, anonymous, and unanimous social choice rule exists if and only if the preference space is contractible. The author gives very clear descriptions of both the social choice theory and the topological background required to prove the theorem. The author also discusses more recent refinements of this central result and the work of Baryshnikov on `topologizing' the discrete Arrovian model. Towards the end of the paper, the author outlines some other recent results in topological social choice theory. The paper focuses on the applications of homotopy theory to social choice, but at the end, the author indicates some possible uses of other areas in topology. The paper serves as an admirable introduction to the field. It could be read profitably both by workers in social choice theory wanting to acquire some useful topology, and by topologists interested in applications of their field to an area few of them often visit. The 75 references provide a good entry to the field for those wishing to pursue their interests further.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 55P99
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 1491045
zbMATH Keywords: topological social choice
zbMATH Keywords: homotopy
zbMATH Keywords: anonymity
reviewed by: Duncan J. Melville
MaRDI profile type: Publication
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