This book captures much of the excitement of current research in utility theory. The book was written in conjunction with the Mathematical Sciences Lecture Series that the author presented at Johns Hopkins University in the summer of 1986. Three central questions guide the exposition: (1) What is expected utility theory? (2) What is wrong with it from a rational perspective? and (3) What has been proposed to correct the problems?
Chapter 1 begins with a crisp review of the history of utility theory. The chapter then covers the axioms and fundamental results of von Neumann-Morgenstern utility theory. The chapter concludes with a brief description of research on risk attitudes, multiattribute utility, and other extensions. This chapter is an excellent introduction to utility theory for students and researchers alike.
Chapter 2 is a balanced critique of expected utility theory from an economic and psychological perspective. The chapter opens by examining the distinction between normative and descriptive theory. On one extreme, Bernoulli sees no difference between the two; at the other end, Tversky and Kahneman (1986) argue that “no theory of choice can be both normatively adequate and descriptively accurate”. The author carefully plots his own course between these extremes.
This chapter covers the psychological literature on framing effects, evaluation in terms of gains and losses versus levels of wealth, the transformation of subjective probabilities, and especially the evidence on violations of the independence axiom. The author concludes, “Some people stand by the independence axiom, but many theorists no longer accept its normative inviolability and have replaced it with weaker conditions.”
The discussion on preference cycles, money pumps, and the preference reversal phenomenon is most thought provoking. The author states, “My own view that transitivity can no longer be regarded as a tenet of the normative creed is presently a minority position.” Fishburn’s book helps in understanding this and other normative issues in decision making.
Chapter 3 explores the generalizations of expected utility. The scattering of results across different journals, conference proceedings, working papers, doctoral theses, and unpublished technical reports is a major obstacle in locating recent research. Even if one can find these materials, the marked differences in notation and assumptions make comparisons difficult. Chapter 3 does a fine job of organizing this research into a coherent system and providing a common language for explaining these results.
Chapter 3 summarizes alternatives to expected utility in four categories. The first category of research includes generalizations of the von Neumann-Morgenstern theory made in the 1960s that preserve linearity and transitivity of strict preference, but weaken some of the ordering assumptions. Unlike those in subsequent categories, these theories do not accommodate violations of the independence axiom.
The second category includes Allais’ nonlinear intensity theory, Machina’s smooth preferences, and the decumulative representations by Quiggin, Yaari, and others. The third category considers the weighted utility theory introduced by Chew and MacCrimmon and refined by Chew, Fishburn, Nakamura, Dekel, and others. The fourth category covers nonlinear, nontransitive theory on skew-symmetric bilinear (SSB) representations by Kreweras, Fishburn, and others. This chapter carefully compares the axioms used in costructing each nonlinear theory. Two sections explain how these theories handle various independence violations and intransitivities.
Chapter 4 provides an in-depth treatment of the SSB utility theory. This chapter integrates and explains the many results obtained by the author and others in the last few years. Chapter 5 adds transitivity to the SSB axioms and explores various ways of generating the weighted linear utility representation. Chapter 6 examines how the results on SSB utility and weighted linear utility can be applied to problems in cyclic preferences, social choice theory, noncooperative game theory, multiple attributes, mean value, and risk attitudes. The list is still growing; this chapter suggests many paths for further research.
The first six chapters of this book cover decision making under risk; the remaining three chapters consider decision making under uncertainty. Chapter 7 reviews Savage’s (1954) additive expected utility theory, its antecedents, and related developments. Chapter 8 provides a short critique of this theory to motivate recent generalizations that fall into eight categories. This chapter describes contributions on expected regret theory by Bell and by Loomes and Sugden, the skew-symmetric additive (SSA) theory by Fishburn, the additive SSB theory by Fishburn and LaValle, the dual bilinear utility representations by Luce and Narens, and various nonadditive linear theories by Schmeidler, Gilboa, Wakker, and others. Chapter 9 focuses on extending the SSA and additive SSB theories to additive nontransitive nonlinear representations.
The preface notes that Chapters 1, 2, 3, 7, and 8 form a “book within a book”. This “basic book” offers a broad perspective on the contemporary and classical research in utility theory. The author’s explanations and commentaries provide important insights for fitting the pieces of contemporary research together. The “second book” consisting of Chapters 4, 5, 6, and 9 integrates contributions made primarily by the author into one convenient volume.
This book is essential reading for anyone interested in the rapidly expanding field of utility theory.