This Element offers an accessible but technically detailed review of expected utility theory (EU), which is a model of individual decision-making under uncertainty that is central for both economics and philosophy. The Element's approach falls between the history of ideas and economic methodology. At the historical level, it reviews EU by following its conceptual evolution from its original formulation in the eighteenth century through its transformations and extensions in the mid-twentieth century to its more recent supersession by post-EU theories such as prospect theory. In reconstructing the history of EU, it focuses on the methodological issues that have accompanied its evolution, such as whether the utility function and the other components of EU correspond to actual mental entities. On many of these issues, no consensus has yet been reached, and in this Element the author offers his view on them.
Author(s): Ivan Moscati
Series: Elements in Decision Theory and Philosophy
Publisher: Cambridge University Press
Year: 2023
Language: English
City: Cambridge
Cover
Title page
Copyright page
The History and Methodology of Expected Utility
Contents
1 Introduction
1.1 The Two Faces of EU: Normative and Descriptive
1.2 EU in Economics and Philosophy
1.3 This Element
2 Bernoulli’s EU
2.1 A New Field of Study
2.2 Expected Payoff
2.3 Nicolaus Bernoulli’s Game and Moral Impossibility
2.4 Cramer’s Game and Moral Value
2.4.1 Moral Value
2.4.2 Priority Issues
2.5 Enter Daniel
2.6 Daniel Bernoulli’s emolumentum medium
2.6.1 Some Implications
2.6.2 St. Petersburg Game
2.7 Bernoulli’s EU: Discussion
2.7.1 Explanatory Structure
2.7.2 Objective Probabilities
2.7.3 Benefit of Money
2.7.4 Benefit of Money (Continued)
2.7.5 Mechanism: Multiply and Add
2.7.6 Why the Average?
3 Fortunes and Misfortunes of Bernoulli’s EU
3.1 Early Utility Theory and Its Problems
3.2 Bernoulli’s Theory and Early Utility Analysis
3.3 The Ordinal Turn
3.3.1 Preferences Are Primary
3.3.2 Rankings and Ordinal Utility
3.3.3 Abandoning Diminishing Marginal Utility
3.3.4 Ordinal and Cardinal Utility
3.4 Bernoulli’s Theory and the Ordinal Turn
4 Von Neumann and Morgenstern’s EU: Presentation
4.1 Lotteries
4.2 Preference As a Binary Relation
4.3 Axioms
4.3.1 Completeness and Transitivity
4.3.2 Continuity
4.3.3 Reduction of Compound Lotteries
4.3.4 Independence Axiom
4.3.5 Independence Axiom versus Additivity Assumption
4.4 The EU Theorem
4.5 Two Comments
5 Von Neumann and Morgenstern’s EU: Discussion
5.1 Explanatory Structure and Decision Mechanism
5.1.1 Unexplained Risk Preferences
5.1.2 A Preference-Based Mechanism
5.2 Risk Attitudes
5.3 The Descriptive and Normative Validity of the Axioms
5.3.1 Independence Axiom
5.3.2 The Allais Paradox
5.3.3 Completeness
5.3.4 Transitivity
5.3.5 Continuity
5.3.6 Reduction
5.4 Stability Issues
5.4.1 Temporal Stability
5.4.2 Stability across Choice Domains
5.4.3 Stability across Elicitation Methods
5.4.4 Completeness, Transitivity, and Stability: Summing Up
5.5 The Descriptive Validity of EU As a Whole
5.5.1 Testing EU: Theory
5.5.2 Testing EU: History
5.6 The Interpretation of euðxÞ
5.6.1 Two Distinct Functions
5.6.2 Why euðxÞ and uðxÞ Are Distinct
5.7 Cardinal and Ordinal Utility, Reloaded
5.7.1 No Way Back
5.7.2 A Novel Understating of Measurement
5.7.3 A Happy Cohabitation
5.8 The As-If Interpretation of EU
5.9 The Status of the Components of von Neumann
and Morgenstern’s EU
6 Savage’s EU
6.1 Two Approaches, One Definition
6.2 The Intuitive-Probability Approach
6.3 The Preference-Based Approach
6.3.1 A Criticism of Intuitive Probabilities
6.3.2 How the Preference-Based Approach Works
6.4 Savage’s Axioms
6.4.1 P1
6.4.2 P2
6.4.3 P3
6.4.4 P4
6.4.5 P5–P7
6.5 Savage’s Theorem and Its Interpretation
6.5.1 Statement
6.5.2 Interpretation
6.5.3 Probability First
6.6 The Ellsberg Paradox
6.6.1 Ellsberg’s Urn
6.6.2 Normativity Issues and Ambiguity Aversion
6.7 State-Dependent Preferences
6.7.1 The Loving Husband’s Bet
6.7.2 Variations of the Story
6.8 The Status of the Components of Savage’s EU
7 Beyond EU: Prospect Theory
7.1 Prospect Theory, Original Version
7.1.1 The Value Function vðyÞ
7.1.2 The Weighting FunctionwðpÞ
7.1.3 The OPT Formula
7.1.4 The Allais Paradox Reconsidered
7.1.5 Risk Attitudes within OPT
7.1.6 Criticisms of OPT
7.2 Cumulative Prospect Theory
7.2.1 Ranks and Cumulative Probabilities
7.2.2 Weighting Cumulative Probabilities
7.2.3 Decision weights in CPT
7.2.4 The CPT Formula
7.2.5 Allais, Ellsberg, and Risk Attitudes in CPT
7.2.6 Criticisms of CPT
7.3 The As-If Interpretation of Prospect Theory
8 A Very Short Conclusion
References
Acknowledgments
