Topological structure of a space of continuous preferences as a space of retractions and the aggregation problem
type: Item
instance of: scholarly article
title: Topological structure of a space of continuous preferences as a space of retractions and the aggregation problem
zbMATH Open document ID: 0642.90012
DOI: 10.1016/0165-4896(87)90033-3
author: B. George
published in: Mathematical Social Sciences
publication date: 1987-01-01T00:00:00Z
review text: This paper shows that a procedure introduced by \textit{G. Chichilnisky} [Adv. Math. 37, 165-176 (1980; Zbl 0446.90004)], can well be used for preferences that are continuous and admit thick indifference classes and satiation points. We study two interrelated problems, (i) the choice of an appropriate topology for a class of preferences and (ii) the topological structure of the preference space. We show that the choice of the Kannai topology is adequate since it makes the preference space complete and Hausdorff. We also show that this topology coincides, on this space, with the closed convergence topology and that the conditions of \textit{G. Chichilnisky} and \textit{G. Heal} [J. Econ. Theory 31, 68-87 (1983; Zbl 0519.90012)] for the existence of continuous, anonymous and unanimous aggregation rules are met.
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 4047380
zbMATH Keywords: retraction
zbMATH Keywords: contractible space
zbMATH Keywords: thick indifference classes
zbMATH Keywords: satiation points
zbMATH Keywords: Kannai topology
zbMATH Keywords: preference space
zbMATH Keywords: unanimous aggregation rules
MaRDI profile type: Publication
full work available at URL: 0165-4896(87)90033-3
OpenAlex ID: W2104793728
cites work: Spaces of economic agents
cites work: Social choice and the topology of spaces of preferences
cites work: Continuous Representation of Preferences
cites work: Necessary and sufficient conditions for a resolution of the social choice paradox
cites work: Q5624957
cites work: Q5520521
cites work: Continuity Properties of the Core of a Market
cites work: Topological aggregation of inequality preorders
cites work: Construction of a continuous utility function for a class of preferences
description: scientific article; zbMATH DE number 4047380