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.
Author(s): Ken Binmore
Edition: 1
Year: 2008
Language: English
Pages: 213
Cover
Title Page
Copyright Page
Acknowledgements
Table of Contents
Preface
1 Revealed Preference
1.1 Rationality?
1.2 Modeling a Decision Problem
1.3 Reason Is the Slave of the Passions
1.4 Lessons from Aesop
1.5 Revealed Preference
1.6 Rationality and Evolution
1.7 Utility
1.8 Challenging Transitivity
1.9 Causal Utility Fallacy
1.10 Positive and Normative
2 Game Theory
2.1 Introduction
2.2 What Is a Game?
2.3 Paradox of Rationality?
2.4 Newcomb’s Problem
2.5 Extensive Form of a Game
3 Risk
3.1 Risk and Uncertainty
3.2 Von Neumann and Morgenstern
3.3 The St Petersburg Paradox
3.4 Expected Utility Theory
3.5 Paradoxes from A to Z
3.6 Utility Scales
3.7 Attitudes to Risk
3.8 Unbounded Utility?
3.9 Positive Applications?
4 Utilitarianism
4.1 Revealed Preference in Social Choice
4.2 Traditional Approaches to Utilitarianism
4.3 Intensity of Preference
4.4 Interpersonal Comparison of Utility
5 Classical Probability
5.1 Origins
5.2 Measurable Sets
5.3 Kolmogorov’s Axioms
5.4 Probability on the Natural Numbers
5.5 Conditional Probability
5.6 Upper and Lower Probabilities
6 Frequency
6.1 Interpreting Classical Probability
6.2 Randomizing Devices
6.3 Richard von Mises
6.4 Refining von Mises’ Theory
6.5 Totally Muddling Boxes
7 Bayesian Decision Theory
7.1 Subjective Probability
7.2 Savage’s Theory
7.3 Dutch Books
7.4 Bayesian Updating
7.5 Constructing Priors
7.6 Bayesian Reasoning in Games
8 Epistemology
8.1 Knowledge
8.2 Bayesian Epistemology
8.3 Information Sets
8.4 Knowledge in a Large World
8.5 Revealed Knowledge?
9 Large Worlds
9.1 Complete Ignorance
9.2 Extending Bayesian Decision Theory
9.3 Muddled Strategies in Game Theory
9.4 Conclusion
10 Mathematical Notes
10.1 Compatible Preferences
10.2 Hausdorff’s Paradox of the Sphere
10.3 Conditioning on Zero-Probability Events
10.4 Applying the Hahn–Banach Theorem
10.5 Muddling Boxes
10.6 Solving a Functional Equation
10.7 Additivity
10.8 Muddled Equilibria in Game Theory
References
Index
