Representing preferences with nontransitive indifference by a single real-valued function
type: Item
instance of: scholarly article
title: Representing preferences with nontransitive indifference by a single real-valued function
zbMATH Open document ID: 0851.90015
DOI: 10.1016/0304-4068(94)00706-G
author: Gianni Bosi
author: Romano Isler
published in: Journal of Mathematical Economics
publication date: 1996-11-25T00:00:00Z
review text: A preference relation on a set \(X\) is a binary asymmetric relation. Interval orders are a class of preference relations. In this paper, the authors consider three classes of interval orders which are complete preorders. They give sufficient conditions for the existence of continuous utility functions representing these complete preorders when \(X\) is a topological space. For this, they use the notion of strong separability introduced by \textit{A. Chateauneuf} [J. Math. Econ. 16, 139-146 (1987; Zbl 0642.90017)]. They also consider the existence of continuous functions representing a strongly separable interval order when \(X\) is a measurable topological space. \{Reviewer's remark: The classes of interval orders introduced by the authors can probably be related to the covering relation and the Gillies relation which are used in the political games literature\}.
Mathematics Subject Classification ID: 91B16
Mathematics Subject Classification ID: 91B08
zbMATH DE Number: 842074
zbMATH Keywords: representation
zbMATH Keywords: interval orders
zbMATH Keywords: complete preorders
zbMATH Keywords: existence of continuous utility functions
reviewed by: Maurice Salles
MaRDI profile type: Publication
cites work: A numerical representation of semiorders on a countable set
cites work: Numerical representation of intransitive preferences on a countable set
cites work: Representing interval orders by a single real-valued function
cites work: Numerical representation of interval orders on a topological space
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cites work: Q5832752
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cites work: Topological Ordered Spaces and Utility Functions
cites work: Existence of an order-preserving function on normally preordered spaces
cites work: Some general theorems on the existence of order-preserving functions
cites work: Q5340517
cites work: The dimension of semiorders
full work available at URL: 0304-4068(94)00706-g
OpenAlex ID: W2003474786
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description: scientific article; zbMATH DE number 842074