Uncertain Decisions: Bridging Theory and Experiments, edited by Luigi Luini,1999, Norwell, Mass.: Kluwer Academic Publishers
Reviewer: Joseph J. Launie, Ph.D., CPCU, Launie Associates, Inc.
Uncertain Decisions, edited by Luigi Luini of the University of Siena, Italy, contains 14 papers presented at the International Summer School of Economic Research, held at the university in July 1995. Luini arranges the papers under four topic headings: Non-expected Utility Theory, Non-expected Utility Applications, New Departures From Classical Decision Theory, and Value to Real World: The Experimental Contribution. Together, the 14 papers provide an excellent summary of decision theory from its classical roots to its present status. As Luini notes in his excellent introduction, these papers examine the relationship between theory and experiments in economic decisions. The result is a reference work on the topic that should find its way into the libraries of insurance professors, economists, and professionals across the spectrum of the social sciences.
In recent years, experimental economists have reported results that are in conflict with expected utility theory, including the Allais and Ellsberg paradoxes. Classical decision theory no longer enjoys a consensus, and decision theory specialists disagree about the most promising new avenues for research. This book shows a field in a state of flux with many new avenues for future research.
In Part I, Aldo Montesano provides a rigorous and systematic set of definitions for vonNeumann-Morgenstern Expected Utility Theory (EUT) and Rank Dependant Utility Theory, which is the most popular nonexpected utility theory, as well as Savage Expected Utility Theory and Choquet Utility Theory This selection, as well as those following, has an excellent set of references enabling the reader to do a thorough review of the literature.
In Part II, John D. Hey describes experiments with risk preference functionals, raising the problem of error evaluation in estimation procedures. He discusses in detail the practical difficulties in consistently interpreting individual mistakes in experiments on decision making.
In Part III, Antoine Billot discusses fuzzy decision theory. He explains that the main purpose of the fuzzy approach of individual preferences is to introduce some new behaviors into the standard theory. In the first part of his article, he presents these new fuzzy behaviors and a new system of preferences. Next, he proves the existence of a utility function translating fuzzy preferences on a convex referential set by means of two different topological notions. Finally, he analyzes the different conditions under which such nonstandard behaviors can be aggregated to give rise to a collective decision. A particularly interesting result is that Billot links Arrow's and May's theorems regarding collective choice in a single approach in which they are special cases.
Itzhak Gilboa and David Scheidler provide an overview of Case-Based Decision Theory (CBDT). This theory postulates that people tend to choose acts that performed well in similar cases in the past. CBDT was originally developed as a theory of decision making under uncertainty. The authors point out that the theory can be viewed as one of repeated choice under certainty and as a foundation for a new theory of consumer behavior. In this section, the authors summarize about six other articles, giving an overview of the CBDT approach.
For the reader who is not a specialist in the area of decision theory, the section by Alessandro Vercelli is particularly useful. He presents recent advances in Decision Theory Under Uncertainty. This is labeled as a nontechnical introduction and is both clearly written and well organized. Vercelli introduces the concept of first- and second-order measures of uncertainty. He defines uncertainty as awareness of ignorance. …