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Axiomatic choice models and duality
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Every day people frequently have to make a choice. For practical and scientific reasons therefore it is interesting to know what choices they make and how they arrive at them. An approach to this question can be made via psychology. However, it is also possible to approach it on a more formal basis. In this book Dr. Wedde- pohl describes the logical structure of an individual's rational choice. It is this formal, logical approach to the decision problem that makes the book interesting reading matter for all those who are engaged in the study of individual choice. The introduction apart this study may be divided into two parts. The first part, consisting of chapters II and III, deals with choice theory on a very abstract level. In chapter II some mathematical concepts are presented and in chapter III two related choice models are treated, the first one based on preferences, the second one on choice functions. The second part consists of chapters IV, V and VI and covers consumer choice theory. After the pre- sentation of the mathematical tools, two models that are extensions of the models of chapter III are dealt with. In the discussion of consumer choice theory the concept of duality plays an important role and it is found that duality is closely related to the notion of favourability introduced in chap- ter II I. Mr. Weddepohl's study forms an introduction to a larger research project to develop the theory of collective choice.
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Table of Contents

I Introduction.- A The subject of the study.- 1.1 The concept of choice.- 1.2 Examples of choice problems in economics.- B The method of the study.- 1.3 Normative and descriptive theories.- 1.4 The axiomatic method.- 1.5 Deduction and induction.- II Mathematical Concepts for Choice Theory.- 2.1 Introduction.- 2.2 Ordering relations.- 2.3 Mappings and correspondences.- 2.4 Maximal elements and greatest elements.- 2.5 Utility functions.- III Choice Models.- 3.1 Introduction.- 3.2 Primitive concepts.- 3.3 The axioms of the preference model.- 3.4 Revealed preference.- 3.5 Favourability and revealed favourability.- 3.6 The logical significance of the preference model.- 3.7 A choice function model.- 3.8 The connection between the choice function model and the preference model.- 3.9 Some modifications of the choice function model.- 3.10 Summary of the connections between the models 5.- IV Mathematics for Consumer Choice Theory.- 4.1 Introduction.- 4.2 Sets in real Euclidean space.- 4.3 C.u.p. sets.- 4.4 Duality.- 4.5 A theorem on c.u.p. sets.- 4.6 Some properties of real valued functions.- V A Consumer Preference Model.- 5.1 Introduction.- 5.2 Primitive concepts.- 5.3 The axioms of the consumer preference model.- 5.4 The utility function.- 5.5 The demand function and its connection with the choice function.- 5.6 Preference sets.- 5.7 Duality in consumer choice theory.- 5.8 Preordering of the price space and the dual utility function.- 5.9 Demand functions, price functions and revealed preference relations.- VI A Demand Function Model.- 6.1 Introduction.- 6.2 Primitive concepts.- 6.3 The axioms of the demand function model.- 6.4 Reconstruction of preference sets.- 6.5 The axioms of the consumer preference model as theorems in the demand function model.- References.

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