"Expected Utility" Analysis without the Independence Axiom

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. The Econometric Society is collaborating with JSTOR to digitize, preserve and extend access to Econometrica.Experimental studies have shown that the key behavioral assumption of expected utilitv theory. the so-called independence axiom," tends to be si,stematicallv violated in practice.Such findings would lead us to question the empirical relevance of the large body of literature on the hehavior of economic agents untder uncertainty which uses expected utility analysis. The first purpose of this paper is to demonstrate that the basic concepts, tools, anid results of expected utility analysis do not depend on the independenec axiom, bLut may be derived from the much weaker assumption of smoothness of preferences over alternative probability distributions. The second purpose of the paper is to show that this approach may be used to construct a simple model of preferences which ties together a wide body of observed behavior toward risk, including the Friedman-Savage and Markowitz observations, and both the Allais and St. Petersburg Paradoxes. INTRODUCTIONAs AN APPROACIt to the theory of individual behavior toward risk, the expected utility model is characterized by the simplicity and normative appeal of its axioms, the familiarity of the notions it employs (utility functions and mathematical expectation), the elegance of its characterizations of various types of behavior in terms of properties of the utility function (risk aversion by concavity, the degree of risk aversion by the Arrow-Pratt measure, etc.), and the large number of results it has produced. It is thus not surprising that most current theoretical research in the economics of uncertainty, as well as virtually all applied work in the field (e.g. optimal trade, investment, or search under uncertainty)3 is undertaken in the expected utility framework.4 Nevertheless, the expected utility hypothesis is still a particular hypothesis concerning individual preferences over alternative probability distributions over wealth. In the years following its revival by von Neumann and Morgenstern in the Theory of Games and Economic Behavior [99], it became generally recognized that expected utility theory depended crucially on the empirical validity of the anonymous referees, the Editor, and especially Franklin Fisher for helpful comments on this material. They are, of course, not responsible for errors. I am also grateful to the National Science Foundation and the Social Science Research Council for financial support.3See, for example, Helpman and Razin f42] and Levhari and Srinivasan f51]. 4The one significant exception to this statement is the "state preference" approach to behavior toward risk (see, for example, Debreu 118, Ch. 7] o...

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