Decision making with doubt regarding the consequences of an action ∗

Anscombe & Aumann (1963) improved the model developed by von Neumann & Morgenstern (1944) suggesting that the outcome of an act can be a lottery. They showed that if the preference relation of a deci-sion maker obeys several axioms then the latter behaves as if they were maximizing some expected utility. We slightly depart from their defini-tion of acts and consider that, in a given state of Nature, the result of an act is a possibility distribution over outcomes rather than a probability distribution. We then extend the work by? to a more general setting. One can consider our contribution as a refinement of a model developed by Ghirardato (2001): the latter models the consequence of an act as a list of possible outcomes. We add to the list of possible outcomes some structure, namely a qualitative structure. We show that if the preference relation a decision maker may have obeys several restrictions, their choices ensue from the maximization of a – qualitative – expected utility