Rational Decisions (ebook)

Argumento de Rational Decisions (ebook)

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds.

The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies.

Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.

"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

"[T]he book constitutes an interesting contribution to this area of research rewarding for philosophers, economists, psychologists, and mathematicians alike."--Reinhard Slick, Mathematical Reviews

"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

"Ken Binmore is one of our deepest thinkers on the foundations of economics and game theory. Here he gives us his personal take on standard decision theory and his own extension of the theory to the case in which decision makers cannot assign unambiguous probabilities to future events. This book will be of considerable interest to economists and philosophers alike."--Eric Maskin, Nobel Prize-winning economist

"Strong on ideas and opinions but low on jargon, this is one of the most lively discussions of the strengths and limitations of the Bayesian approach to decision making that I have ever come across. Clearly and strongly argued, controversial, and a pleasure to read."--Riccardo Rebonato, author of The Plight of the Fortune Tellers

"Ken Binmore's new book on rational decisions is a superb up-to-date introduction to the now large and complex literature of this subject. The touch is light, but the examples and theorems are precise. The references are more than ample to lead the reader to more details on those parts of the subject that are of most interest. Although the author is an economist, the content will appeal to philosophers, psychologists, and statisticians as well."--Patrick Suppes, Stanford University

"Well-written, with many nice illustrative examples, this book contributes to the ongoing debate on whether the Bayesian method is the proper normative framework for making decisions and updating beliefs. The book is extremely impressive in its breadth of cited references: historical, mathematical, philosophical, and statistical."--Mark Machina, University of California, San Diego

"This book takes the reader from the very beginnings of decision theory through innovative new work, and it is written concisely and clearly enough to make the journey seem effortless. It will be essential reading for decision theorists and economists in general, whether new to the field or old hands."--Larry Samuelson, Yale University

"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."--José Luis Bermúdez, Economics and Philosophy0Preface 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