Randomization and Dynamic Consistency

Rai¤a (1961) has suggested that ambiguity aversion will cause a strict preference for randomization. We show, however, that dynamic consistency implies that individuals will be indi¤erent 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 Re‡ection paradox and the 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. Address for Correspondence David Kelsey, Department of Economics, University of Exeter, Rennes Drive, Exeter EX4 4PU, UK. Keywords ambiguity, ex ante and ex post randomization, dynamic consistency, re‡ection paradox, smooth ambiguity. JEL Classi…cation: D81 Research supported by a Leverhulme Research Fellowship. We would like to thank Peter Klibano¤, Tigran Melkonyan, Zvi Safra, Peter Wakker and a seminar audiences at the universities of Bristol, Cergy-Pontoise, Exeter, LSE and RUD 2013 for helpful comments.