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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. This paper addresses two related issues: (a) the "preference reversal" phenomenon and transitivity of preferences and (b) the observability of preference relations by experimental methods.In the first part, we adopt the framework of the theory of expected utility with rankdependent probabilities to show that the well known "preference reversal" phenomenon can be consistent with transitive preferences. When this phenomenon is consistent with transitive preferences, it violates the von Neumann-Morgenstern independence axiom. Consequently, the "preference reversal" phenomenon may be explicated by other nonexpected utility theories.The experiments that produced the evidence on "preference reversal" attempted to elicit the certainty equivalents of given lotteries. The second part of this paper shows that the experimental design used in many of these experiments will elicit the certainty equivalents of given lotteries if and only if the respondent's preferences can be represented by expected utility functionals. Furthermore, we show that a more general class of experiments is not immune to "preference reversal" if non-expected utility preferences are admitted.

This article introduces a new approach to modeling the expanding universe of decision makers in the wake of growing awareness, and invokes the axiomatic approach to model the evolution of decision makers' beliefs as awareness grows. The expanding universe is accompanied by extension of the set of acts, the preference relations over which are linked by a new axiom, invariant risk preferences, asserting that the ranking of lotteries is independent of the set of acts under consideration. The main results are representation theorems and rules for updating beliefs over expanding state spaces and events that have the flavor of "reverse Bayesianism." (JEL D81, D83)According to the Bayesian paradigm, as new discoveries are made and new information becomes available, the universe shrinks: with the arrival of new information, events replace the prior universal state space to become the posterior state space, or universe of discourse. This process of "destruction" reflects the impossibility, in the Bayesian framework, of expanding the state space and of updating the probabilities of null events, coupled with the fact that conditioning on new information renders null events that, a priori, were nonnull. Yet, experience and intuition alike contradict this view of the world. Becoming accustomed to possibilities that were once inconceivable is part of history and our own life experience. There is a sense, therefore, in which our universe expands as we become aware of new opportunities.In this paper we take a step toward modeling the process of growing awareness and expansion of the universe, or state space, in its wake. 1 To model the evolution of beliefs in response to growing awareness, we invoke the theory of choice under uncertainty; borrowing its language and structure while modifying it to fit our purpose. In particular, we allow for new consequences and feasible acts to be discovered and for new evidence to establish, in the mind of decision makers, new links between acts and consequences. The interpretation of the updating is somewhat different for the discovery of new feasible acts and consequences on the one hand 1 Dekel, Lipman, and Rustichini (1998) argue that standard state spaces preclude unawareness. A choice theoretic approach therefore needs a more general point of departure than Savage (1954) and Anscombe and Aumann (1963).

This paper reports the results of a series of experiments designed to test whether and to what extent individuals succumb to the conjunction fallacy. Using an experimental design of Tversky and Kahneman (1983), it finds that given mild incentives, the proportion of individuals who violate the conjunction principle is significantly lower than that reported by Kahneman and Tversky. Moreover, when subjects are allowed to consult with other subjects, these proportions fall dramatically, particularly when the size of the group rises from two to three. These findings cast serious doubts about the importance and robustness of such violations for the understanding of real-life economic decisions.

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