Ordering Ambiguous Acts

Abstract

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 define two notions of more ambiguous with respect to such a class. A more ambiguous (I) act makes an ambiguity averse decision maker (DM) worse off but does not affect the welfare of an ambiguity neutral DM. A more ambiguous (II) act adversely affects 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 indifference of ambiguity neutral elements to the acts being compared. Second, we implement the abstract definitions to characterize more ambiguous (I) and (II) for two explicit preference families: α-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 defined on statistical experiments by Blackwell (1953) and others. Fourthly, we give applications to defining ambiguity “in the small” and to the comparative statics of more ambiguous in a standard portfolio problem and a consumption-saving problem.

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