By Josef Gruber (auth.), Dr. Dr. habil. Andranik Tangian, Prof. Dr. Josef Gruber (eds.)
For numerous a long time, students have built equipment for fixing optimization difficulties which emerge in economics, econometrics, operations learn, and different disciplines. a substantial attempt has been made to build equations from which constraints will be derived, yet strangely little has been performed to build the opposite a part of optimization versions: the scalar-valued aim functionality, the restricted greatest or minimal of which provides the optimum answer. The given quantity is meant to draw consciousness to the matter, to provide the foremost achievements within the box and to stimulate additional examine and teaching.
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Extra info for Constructing Scalar-Valued Objective Functions: Proceedings of the Third International Conference on Econometric Decision Models: Constructing Scalar-Valued Objective Functions University of Hagen Held in Katholische Akademie Schwerte September 5–8, 1995
Based on our (1985) paper we give a comprehensible answer for cases of rational and strongly rational choice. In particular, we formulate the conditions under which a strongly rational choice is generated by a utility function. s: Rational choice, standard choice, pseudotransitivity, convex conditions, star-shaped relation. 1 Introduction One of the main problems of choice theory is to establish a correspondence between adecision maker's preference R and his choice C of best alternatives. They constitute a kind of internal and external descriptions of choice.
O 52 Andrey V. J. (1959): "Rational Choice Functions and Orderings," Economica, 26, 121-127. HANSSON, B. (1968): "Choice Structures and Preference Relations," Synthese, 18, 443-458. S. (1950): "Revealed Preference and the Utility Function," Economica, 17, 159-174. MALlSHEVSKI, A. V. (1993): "Criteria for Judging the Rationality of Decisions in the Presence of Vague Alternatives," Mathematical Sodal Sciences, 26, 205-247. G. (1979): Group Choice. New York, Wiley. K. (1966): "Revealed Preference Theory," Econometrica, 34, 635-645.
Here we follow the method of Richter (1966, 1971) which simultaneously provides a criterion for the existence of an objective function demanded where such a function is built explicitly. Thus, such a criterion will have a desirable constructive form. To this end, introduce another axiomatic condition. 3. (Revealed Value (RV». For every X EU (9) F(X) $ ~~fF(Z) , where f F: U -- IR? is the revealed objective function defined by fF(Z) = min Y::IIEYEU F(Y). (10) The revealed value condition is obviously equivalent to the following functional inequality for F: F(X) It is easy to see also that < max min - :ilEX Y::IIEYEU (11) F(Y).
Constructing Scalar-Valued Objective Functions: Proceedings of the Third International Conference on Econometric Decision Models: Constructing Scalar-Valued Objective Functions University of Hagen Held in Katholische Akademie Schwerte September 5–8, 1995 by Josef Gruber (auth.), Dr. Dr. habil. Andranik Tangian, Prof. Dr. Josef Gruber (eds.)