Uncertainty aversion and aversion to increasing uncertainty

According to the original Ellsberg (1961) examples there is uncertainty version if the decision maker prefers to bet on an urn of known composition rather than on an urn of unknown composition. According to another definition (Schmeidler, 1989), there is uncertainty aversion if any convex combination of two acts is preferred to the least favorable of these acts. We show that these two definitions differ: while the first one truly refers to uncertainty aversion, the second one refers to aversion to increasing uncertainty. Besides, with reference to Choquet Expected Utility theory, uncertainty aversion means that there exists the core of a capacity, while aversion to increasing uncertainty means that the capacity is convex. Consequently, aversion to increasing uncertainty implies uncertainty aversion, but the opposite does not hold. We also show that a completely analogous situation holds for the case of risk and we define a set of risk and uncertainty premiums according to the previous analysis.