Preferences under ignorance

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially fully ignorant of the payoff associated to each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option once payoffs are learned, the optimal choice rule from sets of alternatives is one that is as if the DM had strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are "right".