This paper contributes to the description of the choice behavior of an individual who, as a result of capacity limitations, is unable to deal with a large number of alternatives and who is also unsure about his most preferred alternative in any given set. Hence, there is a conflict in that the individual wants both to reduce the choice set and to keep as many alternatives as possible. A natural way to solve this conflict is to view the individual as choosing sequentially while giving a weight to each corresponding subset of alternatives. We assume that the weights are defined by Choquet capacities which are independent of the path followed in the choice process. These choice capacities are obtained from a utility defined on the power set of alternatives. This implies that the context, identified as the opportunity set, influences the choice made by the individual. However, the choice capacities are not observable. It is shown that they can be converted into probabilities which have intuitive and appealing properties. In particular, using these probabilities allows for a sensible solution to the blue bus-red bus paradox when the individual has a natural preference for flexibility. Copyright 1999 Academic Press.