Individual Choice Behavior: A Theoretical Analysis Book

1	The Basic Theory	1
A	Introduction	1
1	Probabilistic vs. Algebraic Theories	2
2	Multiple Alternative Choices	3
3	Well-Defined Sets of Alternatives	3
B	Probability Axioms	4
C	Choice Axiom	5
1	Statement of Axiom	5
2	Discussion	6
3	Previous Work	10
4	Direct Empirical Testing of Axiom 1	12
D	Two Consequences	16
1	Statement	16
2	Discussion	17
3	Coombs' Data	19
E	Ratio Scale	20
1	Background	20
2	Existence Theorem	23
3	Extension of [upsilon]-Scale	24
4	Previous Work	27
F	Independence-of-Unit Condition	28
1	Statement of Condition	28
2	Behavioral Continuity	29
3	Response Bias	30
4	Estimation of Parameters	32
G	Algebraic Approximations	34
1	Just Noticeable Differences	34
2	The Trace	36
2	Applications to Psychophysics
A	Fechner's Problem	38
1	The Fechnerian Assumption	38
2	Derivation of Fechner's Assumption	39
3	Uniqueness of the Logistic Curve	41
B	The Power Law	42
1	Derivation of the Law	42
2	Estimation of Exponent	44
3	An Alternative Approach	44
4	Two Other Scales	45
C	Interaction of Continua	47
1	Introduction	47
2	Form of [upsilon]([chi], [xi])	49
3	Generalizations	51
4	A Numerical Example	52
5	The Power Law Exponent	53
D	Discriminal Processes	54
1	Introduction	54
2	Relation of Axiom 1 to Thurstone's Case V	55
3	A Generalization to Three or More Alternatives	56
E	Signal Detectability Theory	58
1	Introduction	58
2	Yes-No Experiments	59
3	Forced-Choice Experiments	62
4	Expected-Value Model	63
5	Recognition Experiments and Maximum Amounts of Information Transmitted	64
F	Rank Orderings	68
1	Direction of Ranking	69
2	Inferring Pairwise Probabilities	70
3	Applications to Utility Theory
A	Introduction	75
B	Decomposable Preference Structures	78
1	Definitions	78
2	The Principal Result	79
3	Discussion	82
C	Additional Axioms	83
1	Existence of Three Event Classes	83
2	Restrictions on P(a, b)	85
D	A Proposed Experiment	86
1	A Prediction	86
2	Experimental Implication	87
3	A Utility Decomposition	88
4	Applications to Learning
A	Introduction	91
B	Response Strength Operators	93
C	Alpha Model	96
D	Beta Model	99
1	Axiomatic Derivation	99
2	Simple Beta Model	101
3	Testing the Two-Alternative Beta Model	102
E	Gamma Model	105
F	Application of the Three Models to a Special Case	106
1	Introduction	106
2	Partial Reinforcement	107
3	Alpha Model	108
4	Beta Model	109
5	Gamma Model	110
6	Conclusions	110
G	Some Asymptotic Properties of the Beta Model	111
1	Introduction	111
2	Relations Among Asymptotic Expectations	114
3	Existence and Values of [characters not reproducible] E([upsilon subscript n]) and [characters not reproducible] E(1/[upsilon subscript n])	117
4	A Special Case	120
5	Summary and conclusions
A	Summary	126
B	Conclusions	131
Appendix 1	Alternative Forms of Axiom 1	135
Appendix 2	Form of Latency Distribution	137
Appendix 3	Maximum Likelihood Equations for the Two-alternative, Two-outcome Beta Learning Model	139
Appendix 4	Open Problems	142
A	Conceptual and Empirical	142
B	Mathematical	144
	Bibliography	147
	Index	151