Individual Choice Behavior A Theoretical

This influential treatise presents upper-level undergraduates and graduate students with a mathematical analysis of choice behavior. It begins with the statement of a general axiom upon which the rest of the book rests; the following three chapters, which may be read independently of each other, are devoted to applications of the theory to substantive problems: psychophysics, utility, and learning. Applications to psychophysics include considerations of the Fechnerian assumption and signal detectability theory; discussion of utility theory features unusual results that suggest an experiment to test the theory; and learning-related topics analyze stochastic theories as the basic approach. 1959 ed.

The Basic Theory

1

(134)

Introduction

1

(3)

Probabilistic vs. Algebraic Theories

2

(1)

Multiple Alternative Choices

3

(1)

Well-Defined Sets of Alternatives

3

(1)

Probability Axioms

4

(1)

Choice Axiom

5

(11)

Statement of Axiom

5

(1)

Discussion

6

(4)

Previous Work

10

(2)

Direct Empirical Testing of Axiom 1

12

(4)

Two Consequences

16

(4)

Statement

16

(1)

Discussion

17

(2)

Coombs' Data

19

(1)

Ratio Scale

20

(8)

Background

20

(3)

Existence Theorem

23

(1)

Extension of v-Scale

24

(3)

Previous Work

27

(1)

Independence-of-Unit Condition

28

(6)

Statement of Condition

28

(1)

Behavioral Continuity

29

(1)

Response Bias

30

(2)

Estimation of Parameters

32

(2)

Algebraic Approximations

34

(4)

Just Noticeable Differences

34

(2)

The Trace

36

(2)

Applications to Psychophysics

Fechner's Problem

38

(4)

The Fechnerian Assumption

38

(1)

Derivation of Fechner's Assumption

39

(2)

Uniqueness of the Logistic Curve

41

(1)

The Power Law

42

(5)

Derivation of the Law

42

(2)

Estimation of Exponent

44

(1)

An Alternative Approach

44

(1)

Two Other Scales

45

(2)

Interaction of Continua

47

(7)

Introduction

47

(2)

Form of v(x, ξ)

49

(2)

Generalizations

51

(1)

A Numerical Example

52

(1)

The Power Law Exponent

53

(1)

Discriminal Processes

54

(4)

Introduction

54

(1)

Relation of Axiom 1 to Thurstone's Case V

55

(1)

A Generalization to Three or More Alternatives

56

(2)

Signal Detectability Theory

58

(10)

Introduction

58

(1)

Yes-No Experiments

59

(3)

Forced-Choice Experiments

62

(1)

Expected-Value Model

63

(1)

Recognition Experiments and Maximum Amounts of Information Transmitted

64

(4)

Rank Orderings

68

(7)

Direction of Ranking

69

(1)

Inferring Pairwise Probabilities

70

(5)

Applications to Utility Theory

Introduction

75

(3)

Decomposable Preference Structures

78

(5)

Definitions

78

(1)

The Principal Result

79

(3)

Discussion

82

(1)

Additional Axioms

83

(3)

Existence of Three Event Classes

83

(2)

Restrictions on P(a, b)

85

(1)

A Proposed Experiment

86

(5)

A Prediction

86

(1)

Experimental Implication

87

(1)

A Utility Decomposition

88

(3)

Applications to Learning

Introduction

91

(2)

Response Strength Operators

93

(3)

Alpha Model

96

(3)

Beta Model

99

(6)

Axiomatic Derivation

99

(2)

Simple Beta Model

101

(1)

Testing the Two-Alternative Beta Model

102

(3)

Gamma Model

105

(1)

Application of the Three Models to a Special Case

106

(5)

Introduction

106

(1)

Partial Reinforcement

107

(1)

Alpha Model

108

(1)

Beta Model

109

(1)

Gamma Model

110

(1)

Conclusions

110

(1)

Some Asymptotic Properties of the Beta Model

111

(15)

Introduction

111

(3)

Relations Among Asymptotic Expectations

114

(3)

Existence and Values of lim n → ∞ E(vn) and lim n → ∞ E(1/vn)

117

(3)

A Special Case

120

(6)

Summary and Conclusions

Summary

126

(5)

Conclusions

131

(4)

Appendix 1. Alternative Forms of Axiom 1

135

(2)

Appendix 2. Form of Latency Distribution

137

(2)

Appendix 3. Maximum Likelihood Equations for the Two-alternative, Two-outcome Beta Learning Model

139

(3)

Appendix 4. Open Problems

142

(5)

Conceptual and Empirical

142

(2)

Mathematical

144

(3)

Bibliography

147

(4)

Index

151

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Individual Choice Behavior A Theoretical Analysis

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Table of Contents

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