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.