Mark J. Nachina1 GENERALIZED EXPECTED UTILITY ANALYSIS AND THE NATURE OF OBSERVED VIOLATIONS OF THE INDEPENDENCE AXIOM

First expressed by Allais in the early fifties, dissatisfaction with the expected utility model of individual risk taking behavior has mushroomed in recent years, as the number of papers in this volume, its predecessor (Allais & Hagen(l979», and elsewhere2 indicates. The nature of the current debate, i.e. whether to reject a theoretically elegant and heretofore tremendously useful descriptive model in light of accumulating evidence against its underlying assumptions, is a classic one in science, and the spur to new theoretical and empirical research which it is offering cannot help but leave economists, psychologists, and others who study this area with a better understanding of individual behavior toward risk. In terms of its logical foundations, the expected utility model IDay be thought of as following from three assumptions concerning the individual's ordering of probability distributions over wealth: completeness (i.e. any two distributions can be compared), transitivity of both strict and weak preference, and the so-called "independence axiom." This latter axiom, really the cornerstone of the theory, may be stated as "a risky prospect A is weakly preferred (i.e. preferred or indifferent) to a risky prospect B if and only if a p:(l-p) chance of A or C respectively is weakly preferred to a p:(l-p) chance of B or C, for arbitrary positive probability p and risky prospects A, B, and C." While the first two assumptions serve to imply that the individual's preferences may be represented by a real-valued maximand or "preference functional" defined over probability distributions, it is the independence axiom which gives the theory its main empirical content by placing a restriction on the functional form of the preference functional, implying that it (or some monotonic transformation of it) must be "linear in the probabilities" and hence representable as the mathematical expectation of some von Neumann-Morgenstern utility index defined over the set of pure outcomes. Although the normative validity of the independence axiom