"...During this period there has been a growing awareness-stimulated in large part by Maurice Allais's work in the early 1950s-that people's reasoned judgments often violate the basic assumptions of expected utility. Numerous studies have demonstrated that such violations tend to follow systematic and predictable patterns. Investigators have therefore proposed alternative theories of rational preference that accommodate systematic departures from expected utility while retaining much of its mathematical elegance and computational convenience. With the notable exception of Allais's own theory from the early 1950s, most of the alternatives have emerged during the past decade.
This book attempts to make sense of recent and not so recent developments in preference theory for risky and uncertain decisions. It is arranged in two main parts: Chapters 1 through 6 focus on decision under risk, Chapters 7 through 9 on decision under uncertainty. Each main part answers three questions:
1. What is expected utility theory?
2. What is wrong with it from a rational preference perspective?
3. What has been proposed to correct the problems?
Question 1 is dealt with in Chapter 1 for decision under risk (von Neumann and Morgenstern) and in Chapter 7 for decision under uncertainty (Savage). Chapter 2 and the first part of Chapter 8 address question 2. Question 3 is partly answered by surveys of alternative theories of preference in risky situations (Chapter 3) and in uncertain situations (Chapter 8). These five chapters (1-3, 7-8) comprise a book within the book whose purpose is to provide an up-to-date view of expected utility and its alternatives that aims for organizational clarity and inclusiveness."
Author(s): Peter C. Fishburn
Series: Johns Hopkins Series in the Mathematical Sciences, #5
Publisher: The Johns Hopkins University Press
Year: 1988
Language: English
Pages: 272
Tags: mathematics, utility theory, decision theory, game theory, utilitarianism, economics, VNM, risk, nonlinear returns, prospect theory, cognitive biases
- Preface
- Acknowledgments
1. Historical Background: Expected Utility
1.1 Daniel Bernoulli and Gabriel Cramer
1.2 Riskless Utility in Economics
1.3 von Neumann and Morgenstern
1.4 The Linear Utility Theorem
1.5 Alternative Axioms for Linear Utility
1.6 Risk Attitudes
1.7 Multiattribute Linear Utility
1.8 Extensions for Probability Measures
1.9 Summary
2. Critique of Expected Utility
2.1 Normative versus Descriptive Theory
2.2 Framing Effects
2.3 Money
2.4 Probability Transformations, Probability Preferences
2.5 Independence and the Certainty Effect
2.6 Vagueness and Nontransitive Indifference
2.7 Preference Cycles and Money Pumps
2.8 The Preference Reversal Phenomenon
2.9 Non-Archimedean Preferences
2.10 Summary
3. Generalizations of Expected Utility
3.1 Alternatives to Expected Utility
3.2 Relaxations that Preserve Linearity
3.3 Allais's Nonlinear Intensity Theory
3.4 Smooth Preferences
3.5 Decumulative Representations
3.6 Weighted Utility Theory
3.7 Transitive Convexity
3.8 Nontransitive Convexity
3.9 SSB Utility Theory
3.10 Accommodation of Independence Violations
3.11 Intransitivity Accommodation
3.12 Summary
4. Nontransitive Nonlinear Utility Theory
4.1 The SSB Theorem
4.2 Preliminary Lemmas
4.3 Nontransitive Convex Utility
4.4 Further Implications of C1 and C2
4.5 Implications of Symmetry
4.6 Partial Construction of
4.7 Proof Completion
4.8 Extension for Probability Measures
5. Transitive Nonlinear Utility Theory
5.1 Transitive Convex Utility
5.2 The Need for Countable Boundedness
5.3 Weighted Linear Utility
5.4 Sufficiency Proof
5.5 Weighed Linear Uniqueness
5.6 Equivalent Axiom Sets
5.7 Extension for Probability Measures
6. Applications for Choice Theory and Risk
6.1 von Neumann's Minimax Theorem
6.2 Choice with Cyclic Preferences
6.3 Social Choice Lotteries
6.4 Choice among Choice Contexts
6.5 Nash Equilibria in Noncooperative Games
6.6 Multiple Attributes
6.7 Mean Value and Certainty Equivalence
6.8 Stochastic Dominance
6.9 Risk Attitudes
7. Additive Expected Utility
7.1 Decision under Uncertainty
7.2 Additive Subjective Probability
7.3 Proof of Savage's Probability Theorem
7.4 Additive Expected Utility
7.5 Comments on Savage's Representation Proof
7.6 Additive Linear Utility
7.7 Additive Linear Utility Proofs
7.8 Summary
8. Generalizations of Additive Expected Utility
8.1 Critique of Additive Expected Utility
8.2 Nonadditive Subjective Probability
8.3 Generalizations of Additive Expected Utility
8.4 Additive Nonexpected Intensive Utility
8.5 Expected Regret Theory
8.6 SSA Utility Theory
8.7 Additive SSB Utility
8.8 Nonadditive Linear Utility
8.9 Nonadditive Expected Utility
8.10 Nonadditive Biexpected Utility
8.11 Nonadditive, Nontransitive Theories
8.12 Summary
9. Additive Nontransitive Nonlinear Utility
9.1 Skew-Symmetric Additive Utility
9.2 SSA Utility Proof
9.3 Extension for Nonsimple Acts
9.4 Additive SSB Utility
9.5 Additive SSB Proofs
9.6 Additive SSB Extension
9.7 Extension Proofs
- References
- Index
