
Representations of Preferences Orderings
Springer (Publisher)
Published on 6. April 1995
Book
Paperback/Softback
X, 165 pages
978-3-540-58839-9 (ISBN)
Description
A basic assumption made by pioneers of classical microeconomics such as Edgeworth and Pareto was that the ranking of a consumer's preferences could always be measured numerically, by associating to each possible con- sumption bundle a real number that measured its utility: the greater the utility, the more preferred was the bundle, and conversely. It took several decades before the naivety of this assumption was seriously challenged by economists, such as Wold, attempting to find conditions under which it could be justified mathematically. Wold's work was the first in a long chain of results of that type, leading to the definitive theorems of Debreu and oth- ers in the 1960s, and subsequently to the refinements and generalisations that have appeared in the last twenty-five years. Out of this historical background there has appeared a general mathe- matical problem which, as well as having applications in economics, psy- chology, and measurement theory, arises naturally in the study of sets bear- ing order relations: Given some kind of ordenng t on a set 5, fina a real-valued mapping u on 5 such that for any elements x, y of 5, x t yif and only if u(x) 2: u(y).
If also 5 has a topology (respective/y, differential structure), find conditions that ensure the continuity (respectively, differentiability) of the mapping u. A mapping *u of this kind is called a representation of the ordering C:::.
If also 5 has a topology (respective/y, differential structure), find conditions that ensure the continuity (respectively, differentiability) of the mapping u. A mapping *u of this kind is called a representation of the ordering C:::.
More details
Series
Edition
1995 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
X, 165 p.
Dimensions
Height: 203 mm
Width: 127 mm
Thickness: 10 mm
Weight
196 gr
ISBN-13
978-3-540-58839-9 (9783540588399)
DOI
10.1007/978-3-642-51495-1
Schweitzer Classification
Persons
Prof. Douglas S. Bridges is a professor of pure mathematics at the University of Canterbury. His research interests include the constructive foundations of analysis and topology; mathematical economics; computability and abstract complexity theory; and quantum logic. He has published many related articles and papers, among his 8 authored books are "Computability: A Mathematical Sketchbook", "Foundations of Real and Abstract Analysis", and "Techniques of Constructive Analysis". He is a Fellow of the Royal Society of New Zealand, and a Corresponding Fellow of the Royal Society of Edinburgh. Dr. Lumini¿a Simona Vî¿¿ is an Adjunct Fellow of the Department of Mathematics and Statistics, University of Canterbury, and a Senior Business Analyst with the New Zealand Customs Service. Her research interests include constructive foundations of analysis and topology, and recursive function theory, computability and complexity. She has published many related articles and papers, and coauthored "Techniques of Constructive Analysis".
Content
1 Ordered Sets and Order Homomorphisms.- 2 Order Homomorphisms in Euclidean Space.- 3 The Fundamental Theorems.- 4 A Miscellany of Representations.- 5 The Urysohn-Nachbin Approach.- 6 Interval Orders.- 7 Differentiable Order Homomorphisms.- 8 Jointly Continuous Order Homomorphisms.- References.