Randomization and Dynamic Consistency

Raiffa (1961) has suggested that ambiguity aversion will cause a strict preference for randomization. We show that dynamic consistency implies that individuals will be indifferent to ex ante randomizations. On the other hand, it is possible for a dynamically-consistent ambiguity averse preference relation to exhibit a strict preference for some ex post randomizations. We argue that our analysis throws some light on the recent debate about paradoxes for the smooth model of ambiguity. We show that these rest on whether the randomizations implicit in the set-up are viewed as being resolved before or after the (ambiguous) uncertainty.