Rational Decisions

Ken Binmore is a mathematician turned economist and philosopher. He has held chairs at the London School of Economics and Political Science as well as other universities, and is professor emeritus of economics at University College London. His recent books include "Natural Justice, Does Game Theory Work?", and "A Very Short Introduction to Game Theory".

"This short, ambitious book is intended to appeal to the presumed curiosity of economists, statisticians, and philosophers as to what constitutes rationality in scientific induction. Binmore, a game theorist aware of the daunting complexity of his subject matter for nonspecialists, has gone to great pains in making his work accessible, even offering marginal symbols to indicate the substantial portions of the text best avoided by readers lacking the author's appetite for mathematical data."--Choice "Rational Decisions contains a wealth of stimulating arguments and thought-provoking claims. It would be an excellent text for an advanced seminar in decision theory, particularly for students with a solid technical background. And no economist, philosopher or political scientist seriously interested in theories of rational decision-making can afford to ignore Binmore's controversial and iconoclastic claims."--Jose Luis Bermudez, Economics and Philosophy "[T]he book constitutes an interesting contribution to this area of research rewarding for philosophers, economists, psychologists, and mathematicians alike."--Reinhard Slick, Mathematical Reviews "It is an original and stimulating book. I enjoyed it very much, and expect that you may too."--Brian Skyrms, British Journal for Philosophy of Science

• 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