Sharing beliefs and the absence of betting in the Choquet expected utility model

Choquet expected utility maximizers tend to behave in a more “cautious” way than Bayesian agents, i. e. expected utility maximizers. We illustrate this phenomenon in the particular case of betting behavior. Specifically, consider agents who are Choquet expected utility maximizers. Then, if the economy is large, Pareto optimal allocations provide full insurance if and only if the agents share at least on prior, i. e., if the intersection of the core of the capacities representing their beliefs is non empty. In the expected utility case, this is true only if they have a common prior. Received: July 2000; revised version: May 2001     

Probabilities as Similarity‐Weighted Frequencies

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the belief formation process follows a simple formula: beliefs are a similarity‐weighted average of the beliefs induced by each past case.     

Cognitive rationality and alternative belief measures

In this article, we first examine the various criticisms of the probabilistic model. Then we introduce capacities in order to show that if a probability measure corresponds to anesthetizing the belief of the agent's knowledge, it is then possible to suggest another type of rationality—namely, being able to describe a wise and a rash behavior when facing risk—and therefore another model of belief under uncertainty. While trying to specify various alternative measures, possibility, necessity, and measures resulting from a triangular norm or from a triangular conorm, we finally try to define the field of application of the probabilistic model as well as a sign of the rationality choice: constraint of mass-unity for traditional rationality, and constraint of duality for the one we present.This article is a revised version of a paper presented during the FUR V Congress, Duke University, North Carolina, USA, June 10–13, 1990. I am indebted to Bertrand Munier, Alain Chateauneuf, Olivier Favereau, Jacques-François Thisse, Bernard Walliser, and Kip Viscusi for helpful comments on earlier versions of this article.     

The Deep Side of Preference Theory

An individual is said to have a taste for a particular menu, i.e. a subset of available commodities, if he is indifferent between all commodity bundles that contain the same quantity for each commodity which actually is in the menu, whatever the rest of the bundle. Then, a taste is directly defined as a deep property of preferences. As a first result, it is shown that a complete and transitive preference relation over the commodity bundles is equivalent to regular tastes where regularity means that tastes can be derived from a pure qualitative relation between the different commodities. Besides, a preference family based on preference relations corresponding to each particular commodity is said to be rationalizable if there exists a metapreference over commodity bundles which consistently summarizes the preference family and then allows to decide. As a second result, it is shown that if a preference family is rationalizable, then the tastes are organized thanks to a reflexive and transitive qualitative relation between the different commodities.     

Aggregation of preferences: The fuzzy case

The basic purpose of this paper is to link both theorems of impossibility and existence by introducing fuzzy relations of preference and an exogeneous requirement, the planner's one, and then proving the fundamental part played by the extremist agents, leximin and leximax. In other words, to bring out the link between the planner's requirement and the difficulty of the transition from individual to collective, as well as the theoric relation between this requirement and the extremist agents, we define a fuzzy behavior of preference which allows us to build up two determinant fuzzy coalitions. These coalitions will be the base of the planner's requirement and the link between pessimistic results (Arrow's impossibility) and optimistic ones (May's theorem of majority choice).