A Nonadditive Probability Model of Individual Choice

This paper aims at contributing to the description of the choice behavior of an individual who is unable to deal with a large number of alternatives and is unsure about his most preferred alternative in any given choice subset. Hence, there is a conflict in that the individual wants to reduce the choice set (because of his limitated ability in processing various objects) and to keep as many alternatives as possible (because he is unsure about his own tastes). 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 nonadditive probabilities which are independent of the path followed in the choice process. These nonadditive choice probabilities are constructed from a utility defined on the power set of alternatives; this utility represents a preference for flexibility. However, the nonadditive choice probabilities 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.