Rational Decisions

Preface ix

Chapter 1: Revealed Preference 1
1.1 Rationality? 1
1.2 Modeling a Decision Problem 2
1.3 Reason Is the Slave of the Passions 3
1.4 Lessons from Aesop 5
1.5 Revealed Preference 7
1.6 Rationality and Evolution 12
1.7 Utility 14
1.8 Challenging Transitivity 17
1.9 Causal Utility Fallacy 19
1.10 Positive and Normative 22

Chapter 2: Game Theory 25
2.1 Introduction 25
2.2 What Is a Game? 25
2.3 Paradox of Rationality? 26
2.4 Newcomb's Problem 30
2.5 Extensive Form of a Game 31

Chapter 3: Risk 35
3.1 Risk and Uncertainty 35
3.2 Von Neumann and Morgenstern 36
3.3 The St Petersburg Paradox 37
3.4 Expected Utility Theory 39
3.5 Paradoxes from A to Z 43
3.6 Utility Scales 46
3.7 Attitudes to Risk 50
3.8 Unbounded Utility? 55
3.9 Positive Applications? 58

Chapter 4: Utilitarianism 60
4.1 Revealed Preference in Social Choice 60
4.2 Traditional Approaches to Utilitarianism 63
4.3 Intensity of Preference 66
4.4 Interpersonal Comparison of Utility 67

Chapter 5: Classical Probability 75
5.1 Origins 75
5.2 Measurable Sets 75
5.3 Kolmogorov's Axioms 79
5.4 Probability on the Natural Numbers 82
5.5 Conditional Probability 83
5.6 Upper and Lower Probabilities 88

Chapter 6: Frequency 94
6.1 Interpreting Classical Probability 94
6.2 Randomizing Devices 96
6.3 Richard von Mises 100
6.4 Refining von Mises' Theory 104
6.5 Totally Muddling Boxes 113

Chapter 7: Bayesian Decision Theory 116
7.1 Subjective Probability 116
7.2 Savage's Theory 117
7.3 Dutch Books 123
7.4 Bayesian Updating 126
7.5 Constructing Priors 129
7.6 Bayesian Reasoning in Games 134

Chapter 8: Epistemology 137
8.1 Knowledge 137
8.2 Bayesian Epistemology 137
8.3 Information Sets 139
8.4 Knowledge in a Large World 145
8.5 Revealed Knowledge? 149

Chapter 9: Large Worlds 154
9.1 Complete Ignorance 154
9.2 Extending Bayesian Decision Theory 163
9.3 Muddled Strategies in Game Theory 169
9.4 Conclusion 174

Chapter 10: Mathematical Notes 175
10.1 Compatible Preferences 175
10.2 Hausdorff's Paradox of the Sphere 177
10.3 Conditioning on Zero-Probability Events 177
10.4 Applying the Hahn-Banach Theorem 179
10.5 Muddling Boxes 180
10.6 Solving a Functional Equation 181
10.7 Additivity 182
10.8 Muddled Equilibria in Game Theory 182

References 189
Index 197