Preference for flexibility and the opportunities of choice

A decision-maker exhibits preference for flexibility if he always prefers any set of alternatives to its subsets, even when two of them contain the same best element. Desire for flexibility can be explained as the consequence of the agent's uncertainty along a two-stage process, where he must first preselect a subset of alternatives from which to make a final choice later on. We investigate conditions on the rankings of subsets that are compatible with the following assumptions: (1) the agent is endowed with a VN-M utility function on alternatives, (2) the agent attaches a subjective probability to the survival of each subset of alternatives, and (3) the agent will make a best choice out of any set which becomes available, and ranks sets ex-ante in terms of the expected utility of the best surviving alternatives within them.