Subjective Ambiguity and Preference for Flexibility

This paper studies preferences over menus of alternatives. A preference is monotonic when every menu is at least as good as any of its subsets. The main result is that any numerical representation for a monotonic preference can be written in minimax form. A minimax representation suggests a decision maker who faces uncertainty about her own future tastes and who exhibits an extreme form of ambiguity aversion with respect to this subjective uncertainty. Applying the main result in a setting with a finite number of alternatives leads to a natural weakening of the seminal characterization of preference for flexibility introduced by Kreps (1979). This new characterization clarifies the consequences of his last axiom, ordinal submodularity. While the remaining axioms are equivalent to the existence of a (weakly) increasing aggregator of second period maximal utilities, ordinal submodularity holds if and only if this aggregator can be taken to be strictly increasing.