Ranking opportunity sets on the basis of their freedom of choice and their ability to satisfy preferences: A difficulty

This paper examines a possibility of enlarging the domain of definition of individual preferences suggested by the recent literature on freedom of choice. More specifically, the possibility for an individual to have preferences that depend upon both the opportunity set that she faces and the particular alternative that she chooses from that set is considered. Even more specifically, the possibility for these preferences to value freedom of choice, as defined by the set theoretic relation of inclusion, while being consistent, in a certain sense, with the existence of a preference ordering over the options contained in opportunity sets is investigated. It is shown in the paper that a necessary condition for the existence of any transitive extended preferences of this type is for freedom of choice to be given no intrinsic importance.