Ambiguity, randomization and the timing of resolution of uncertainty

The classic framework of Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) for decision-making under uncertainty postulates both a primary source of uncertainty (the “horse race”) and an auxiliary randomization device (the “roulette wheel”). It also imposes a specific timing of resolution of uncertainty as the horse race takes place before the roulette is played. While this timing is without loss of generality for Subjective Expected Utility, it forbids plausible choice patterns of ambiguity aversion. In this paper, we reverse this timing by assuming that the roulette is played prior to the horse race and we obtain an axiomatic characterization of Choquet Expected Utility that is dual to that of Schmeidler (Econometrica 57(3):571–587, 1989). In this representation, ambiguity aversion is characterized by an aversion to conditioning roulette acts on horse events which, as we argue, is more plausible. Moreover, it can be larger than in Schmeidler’s model. Finally, our reversed timing yields incentive compatibility of the random incentive mechanisms, frequently used in experiments for eliciting ambiguity attitudes.