Probabilistic choice models for uncertain outcomes

This paper discusses the problem of specifying probabilistic models for choices (strategies) with uncertain outcomes. The most general case we consider is choice settings where the uncertain outcomes are sets which may contain more than one alternative. This is of interest for the following type of choice processes that take place in two stages: In stage one the agent has the choice between uncertain sets of alternatives and only knows the probabilities of which alternative that belongs to each set. Conditional on the choice in the first stage the content of the chosen set is revealed and the agent chooses (under perfect certainty) the most preferred one from this set. The standard setting in which the outcomes are single alternatives, follows as a special case of the model.
The point of departure is a generalization of Luce IIA assumption to choice experiments with uncertain outcomes and we analyze the implications when IIA is combined with particular assumptions about invariance with respect to aggregations of strategies.