Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli??s discussion of ??convex Bayesianism?? (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of ??strong independence?? (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli??s results and recent developments on the axiomatization of non-binary preferences, and its impact on ??complete?? independence, are described.