Subjective Timing of Randomization and Ambiguity

Raiffa (1961) criticizes ambiguity-averse preferences by claiming that hedging is possible with randomization of choices. We argue that the timing of randomization is crucial for hedging: If the decision maker thinks that the randomization is ex ante (i.e., before a realization of a state) then it provides no hedging; if it is ex post (i.e., after a realization of a state) then it provides hedging. We investigate the decision maker’s preference over sets of acts among which he can randomize. To capture a preference for randomization, we propose two new axioms. The dominance axiom claims that the decision maker should prefer a set A of acts to another set B if, for any randomization among B, there exists a preferred randomization among A, no matter whether he can randomize ex ante or ex post. The certainty strategic rationality axiom requires that if the decision maker prefers A to B and A consists of a constant act, then he should be indifferent between A and A ∪B because the randomization with the constant act does not provide hedging. By using these ∗I am indebted to my adviser, Eddie Dekel, for continuous guidance, support, and encouragement. I am grateful to Larry Epstein, Federico Echenique, Jeff Ely, Faruk Gul, Pietro Ortoleva, Kyoungwon Seo, and Marciano Siniscalchi for discussions which have led to the improvement of the paper.