The multiple priors of the open-minded decision maker

A multiple-prior decision maker is open-minded if he/she can describe, as subjective uncertainty, all convex sets of distributions over payoff relevant consequences. Theorem 1: open-mindedness is equivalent to the ability to subjectively describe both the uniform distribution on an interval and the set of all distributions on an interval. Theorem 2: sets of priors that fail either condition cannot describe a dense class of problems. The use of open-minded sets of priors to model decision makers allows the objective and the subjective approaches to uncertainty to inform each other. It also changes the implications of previously used axioms for multi-prior preferences because the axioms must apply to a larger set of problems.