Ordering Ambiguous Acts1

We investigate what it means for one act to be more ambiguous than another. The question is evidently analogous to asking what makes one prospect riskier than another, but beliefs are neither objective nor representable by a unique probability. Our starting point is an abstract class of preferences constructed to be (strictly) partially ordered by a more ambiguity averse relation. We de…ne two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse o¤ but does not a¤ect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely a¤ects a more ambiguity averse DM more, as measured by the compensation they require to switch acts. Unlike more ambiguous (I), more ambiguous (II) does not require indi¤erence of ambiguity neutral elements to the acts being compared. Second, we implement the abstract de…nitions to characterize more ambiguous (I) and (II) for two explicit preference families: -maxmin expected utility and smooth ambiguity. Our characterizations show that (the outcome of) a more ambiguous act is less robust to a perturbation in probability distribution governing the states. Third, the characterizations also establish important connections between more ambiguous and more informative as de…ned on statistical experiments by Blackwell (1953) and others. Fourthly, we give applications to de…ning ambiguity "in the small" and to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem. JEL Classi…cation Numbers: C44, D800, D810, G11