Abstract
A kind of inverse problem of scalar optimization is considered. An optimal value function for making an optimal choice from a variable admissible set is given, while the backing objective function being unknown. The first problem is the existence of the objective function whose extremization generates the given opportunity value function. We formulate several axiomatic properties of this value function which are necessary and sufficient for the existence of the objective function. One of these properties implies a construction procedure, and an illustrative example of explicitly constructing an objective function from several choices is considered.
This study was partially supported by the grants ACE-91-R02 of the European Community and 95-01-00057a of the Russian Foundation for Basic Research which are gratefully acknowledged.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arrow, K.J. (1959): “Rational Choice Functions and Orderings,” Economica, 26, 121–127.
Hansson, B. (1968): “Choice Structures and Preference Relations,” Synthese, 18, 443–458.
Houthakker, H.S. (1950): “Revealed Preference and the Utility Function,” Economica, 17, 159–174.
Malishevski, A.V. (1993): “Criteria for Judging the Rationality of Decisions in the Presence of Vague Alternatives,” Mathematical Social Sciences, 26, 205–247.
Mirkin, B.G. (1979): Group Choice. New York, Wiley.
Richter, M.K. (1966): “Revealed Preference Theory,” Econometrica, 34, 635–645.
-(1971): “Rational Choice,” in Preference, Utility, and Demand, ed. by J.S. Chipman, L. Hurwicz, M.K. Richter, and H.F. Sonnenschein. New York: Harcourt Brace Jovanovich, 29–58.
Samuelson, P.A. (1938): “A Note on the Pure Theory of Consumer Behavior,” Economica, 5, 61–71.
-(1950): “The Problem of Integrability in Utility Theory,” Economica, 17, 355–385.
Sen, A.K. (1971): “Choice Functions and Revealed Preference,” Review of Economic Studies, 38, 307–317.
Suzumura, K. (1977): “Houthakker’s Axiom in the Theory of Rational Choice,” Journal of Economic Theory, 14, 284–290.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Malishevski, A.V. (1997). An Axiomatic Justification of Scalar Optimization. In: Tangian, A., Gruber, J. (eds) Constructing Scalar-Valued Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48773-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-48773-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63061-6
Online ISBN: 978-3-642-48773-6
eBook Packages: Springer Book Archive