CONTENTS
1. Introduction = 1
Normative Applications = 4
Descriptive Applications = 5
Problems = 16
2. Preference Relations and Revealed Preference = 7
Binary Relations = 7
Preference Relations = 8
Revealed Preference Theory = 11
Concluding Remarks = 15
Problems = 16
3. Ordinal Utility = 19
Finite X = 19
Countably Infinite X = 22
Uncountable X = 24
Uniqueness = 26
Bells and Whistles = 26
Problems = 28
4. Choice Under Uncertainty : Formulations and Representations = 31
NM Models = 32
Savage Style Models = 33
Anscombe-Aumann = 38
Problems = 39
5. von Neumann-Morgenstern Expected Utility = 43
Finite Prize Spaces = 43
The Mixture Space Theorem = 52
Simple Probability Distributions = 57
Non-simple Probability Measures and the Sure-thing Principle = 59
Bounded Utility = 63
Continuity = 65
Problems = 65
6.Utility Functions for Money = 71
Basic Properties and Definitions = 71
Decreasing, Increasing, and Constant Risk Aversion = 74
Comparison of the Risk Aversion of Two Totreps = 77
Proof of Theorem(6.7) = 80
Relative Risk Aversion = 81
Normative Uses of These Properties = 82
On Descriptive Applications and "Stronger Measures of Risk Aversion = 88
Problems = 92
7. Horse Race Lotteries and Roulette Wheels = 99
The Choice Set = 100
H as a Mixture Space = 102
First Roulette and then the Horses = 105
State Dependent and State Independent Utility = 108
Problems = 111
8. Subjective Probability = 115
Probability Measures = 116
Qualitative Probability = 117
Basics of the Savage Approach = 120
Fine and Tight Qualitative Probabilities = 122
The Savage Theory = 124
Problems = 125
9. Savage's Theory of choice Under Uncertainty = 127
The-Savage Formulation = 127
The Seven Savage Axioms = 128
The Savage Development = 132
Problems = 136
10. Conditional Preference, Conditional Probability, and Contingent Choice = 139
Conditional Preference and Conditional Probability = 139
Choosing as Action Contingent Upon New Information = 141
Problems = 144
11. Independence, Exchangeability, and de Finetti's Theorem = 145
Some Bedtime Reading = 145
de Finetti's Theorem = 157
de Finetti's Theorem as the Fundamental Theorem of(Most) Statistics = 159
Bayesian Inference and de Finetti's Theorem As Normative Decision Tools = 160
Unanimous Priors = 162
Problems = 163
12. Normative Uses of These Models on Subproblems = 165
The Basic Problem = 166
Variation #1 : Statistical Dependence Between x and y = 167
Variation #2 : Discretion as to y = 169
Variation #3 : Temporal Resolution of Uncertainty = 171
Summary = 175
Problems = 176
13. Dynamic Choice Theory and the Choice of Opportunity Sets = 181
Basic Setup = 181
The Standard Model = 183
Changing Tastes and Sophisticated Choice = 185
Preference for Flexibility = 187
Discussion = 189
Problems = 190
14. The Experimental Evidence = 191
The Allais Paradox = 192
The Ellsberg Paradox = 195
Framing Effects = 196
Summary = 198
Problems = 198
References = 201
Index = 205
