The congruence axiom and path independence
type: Item
instance of: scholarly article
title: The congruence axiom and path independence
zbMATH Open document ID: 0957.91036
author: Taradas Bandyopadhyay
author: Kunal Sengupta
published in: Journal of Economic Theory
publication date: 1999-11-11T00:00:00Z
review text: Let \(X\) be a universal set and let \([X]\) denote the collection of non-empty subsets of \(X\). The authors consider choice functions \(C:S \to [X]\), where \(S\) is a non-empty subcollection of \(X\). Let \(A \in S\). A path in \(A\) is a finite ordered collection of non-empty subsets of \(A\) covering \(A\). A choice function is called path independent on \(A\) if the ultimate choice in some sequential procedure does not depend upon the path. In the general setting of the authors, the domain of the choice function may not be all of \([X]\). In this case, it is possible that given a set \(A\in S\), some of the subsets of a path in \(A\), their images under the choice function, or indeed the image of \(A\), may not be in \(S\). Hence, in order to define sequential choice procedures, the authors introduce various technical admissibility criteria. Under these admissibility criteria, the main result of the paper is that a sequential choice function is path independent if and only if it satisfies Richter's congruence axiom on revealed preference, which in turn is a necessary and sufficient condition for \(C\) to have a transitive rationalization.
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 1348018
zbMATH Keywords: choice functions
zbMATH Keywords: path independence
zbMATH Keywords: transitive rationality
zbMATH Keywords: revealed preference
reviewed by: Duncan J. Melville
MaRDI profile type: Publication
full work available at URL: jeth.1999.2520
OpenAlex ID: W2074568629
Wikidata QID: Q114018513
cites work: The Construction of Utility Functions from Expenditure Data
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cites work: Synopses in the Theory of Choice
cites work: On the routewise application of choice
DOI: 10.1006/JETH.1999.2520
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description: scientific article; zbMATH DE number 1348018