Progress In Decision Utility And Risk Theory

In this volume we present some of the papers delivered at FUR-IV - the Fourth International Conference on Founda tions and Applications of Utility, Risk and Decision Theory in Budapest, June 1988. The FUR Conferences have provided an appreciated forum every two years since 1982 within which scientists can report recent issues and prospective applications of decision theory, and exchange ideas about controversial questions of this field. Focal points of the presented papers are: expected utility versus alterna tive utility models, concepts of risk and uncertainty, developments of game theory, and investigations of real decision making behaviour under uncertainty and/or in risky situations. We hope that this sample of papers will appeal to a wide spectrum of readers who are interested in and fami liar with this interesting and exciting issues of decision theory. A wide range of theoretical and practical questions is considered in papers included in this volume, and many of them closely related to economics. In fact, there were two Nobel-Laureates in economics among the participants: I. Herbert A. Simon (1978) and Maurice Allais (1988), who won the prize just after the conference. His paper deals with problems of cardinal utility. After a concise overview of the history and theory of cardinal utility he gives an estimate of the invariant cardinal utility function for its whole domain of variation (i. e.

1. PROGRESS IN UTILITY AND RISK THEORY At the First International Congress of Utility and Risk Theory in Oslo 1982 (FUR-82) it appeared to be a widespread feeling among the participants that the conference signalled something like a paradigm shift in the field. This does not necessarily mean that old truths were discarded and replaced by new ones, but rather that new theories and new empirical evidence were brought forth, compelling old theories to be critically analyzed from new angels. Some of the papers presented at FUR-82 have been published by Reidel in 1983 in a volume edited by Stigum and Wenst0p. The present volume contains com mentaries on a number of the papers presented at the conference together with broader outlines of current views on the theory. The observation that utility and risk theory now appears to be in a state of rapid change has prompted us to choose the title PROGRESS IN UTILITY AND RISK THEORY for the book, in the belief that science always moves from poorer to more advanced paradigms or from weaker to more forceful theories. In other words, change is usually progress, even though intermediate stages in a para digm shift may be bewildering, to say the least.

The Second International Conference on Foundations of Utility and Risk Theory was held in Venice, June 1984. This volume presents some of the papers delivered at FUR-84. (The First International Conference, FUR-82, was held in Oslo and some of the papers presented on that occasion were published by Reidel in the volume Foundations of Utility and Risk Theory with Applications, edited by Bernt P. Stigum and Fred Wenst~p). The theory of choice under uncertainty involves a vast range of controversial issues in many fields like economics, philosophy, psychology, mathematics and statistics. The idea of discussing these problems in international conferences has been successful: two conferences have been held and others will follow. The climate of the debate has changed in the meantime, partly as a result of these conferences. It is no more only a question of attacking or defending the neo-Bernoullian assumptions, but also of proposing wider generalizations and including new elements in the analysis of the decision process. For instance Amartya Sen - comparing the two current notions of rationality, internal consistency and self-interest pursuit introduces the concept of reasoning and considers the irrationality which may result from the failure of a positive correspondence between reasoning and choice or from a limited capacity of reasoning. Rationality is also considered with respect to the controversial axiom of strong independence. John C. Harsanyi introduces the concept of practical certainty, i. e.

Whether we like it or not we all feel that the world is uncertain. From choosing a new technology to selecting a job, we rarely know in advance what outcome will result from our decisions. Unfortunately, the standard theory of choice under uncertainty developed in the early forties and fifties turns out to be too rigid to take many tricky issues of choice under uncertainty into account. The good news is that we have now moved away from the early descriptively inadequate modeling of behavior. This book brings the reader into contact with the accomplished progress in individual decision making through the most recent contributions to uncertainty modeling and behavioral decision making. It also introduces the reader into the many subtle issues to be resolved for rational choice under uncertainty.

Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory

In this valuable book, Paul Schoemaker summarizes recent experimental and field research that he and others have undertaken regarding the descrip tive validity of expected utility theory as a model of choice under uncer tainty. His principal message is that this paradigm is too narrow in its con ception and misses some of the important elements of a descriptive model of individual choice. In particular, Schoemaker calls attention to the impor tance of individual differences, task effects, and context effects as they influence behavior. The expected utility hypothesis has come under scrutiny in recent years from a number of different quarters. This book brings together these many studies and relates them to the large body of literature on individual de cision making under risk. Although this paradigm may be appropriate for describing behavior under many conditions of uncertainty, Schoemaker presents convincing evidence that it does not do well with respect to protec tion against low-probability events. For example, he shows that the insur ance purchase decision is influenced by the way information is presented to the client, as well as by the statistical knowledge of the respondents.

As desired, the infonnation demand correspondence is single valued at equilibrium prices. Hence no planner is needed to assign infonnation allocations to individuals. Proposition 4. For any given infonnation price system p E . P (F *), almost every a E A demands a unique combined infonnation structure (although traders may be indifferent among partial infonnation sales from different information allocations, etc. ). In particular, the aggregate excess demand correspondence for net combined infonnation trades is a continuous function. Proof Uniqueness fails only if an agent can obtain the same expected utility from two or more net combined infonnation allocations. If this happens, appropriate slight perturbations of personal probability vectors destroy the equality unless the utility functions and wealth allocations were independent across states. Yet, when utilities and wealths don't depend on states in S, no infonnation to distinguish the states is desired, so that the demand for such infonnation structures must equal zero. To show the second claim, recall that if the correspondence is single valued for almost every agent, then its integral is also single valued. Finally, note that an upper hemicontinuous (by Proposition 2) correspondence which is single valued everywhere is, in fact, a continuous function. [] REFERENCES Allen, Beth (1986a). "The Demand for (Differentiated) Infonnation"; Review of Economic Studies. 53. (311-323). Allen, Beth (1986b). "General Equilibrium with Infonnation Sales"; Theory and Decision. 21. (1-33). Allen, Beth (1990). "Infonnation as an Economic Commodity"; American Economic Review. 80. (268-273).