Preference for randomization and ambiguity aversion

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. Ex-ante randomizations, which are randomizations before a state is realized, could provide only ex-ante hedging but not ex-post hedging, in contrast to ex-post randomizations, which are randomizations after a state is realized. However, these two randomizations have been assumed to be indifferent under the reversal of order axiom proposed by Anscombe and Aumann (1963). We, therefore, propose a weaker axiom, the indifference axiom, which allows heterogeneous attitudes toward the timing of randomization. By using this new axiom as well as standard axioms, we provide an extension of Gilboa and Schmeidler's (1989) Maxmin preferences that treats a preference for ex-ante randomizations separately from a preference for ex-post randomizations. In the representation, a single parameter characterizes a preference for ex-ante randomizations. By parsimoniously changing only the value of that single parameter, the representation can be consistent with Raiffa's (1961) normative argument as well as recent experimental evidence.