Event-Separability in the Ellsberg urn

Ellsberg's three-color urn involves two distinct sources of uncertainty-the color composition of the urn (which is subjective) and the identity of the drawn ball (which is objective)-and bets on it can involve mixed objective/subjective uncertainty. It is known that typical betting preferences on this urn violate both the Sure-Thing Principle and probabilistic sophistication over its mixed uncertainty but are consistent with both of them over its purely subjective uncertainty. In this paper, we show that the standard Ellsberg-type preference reversal is actually implied by the Independence Axiom over its purely objective uncertainty.