Uncertainty Levels of Second-Order Probability

Since second-order probability distributions assign probabilities to probabilities there is uncertainty on two levels. Although different types of uncertainty have been distinguished before and corresponding measures suggested, the distinction made here between firstand second-order levels of uncertainty has not been considered before. In this paper previously existing measures are considered from the perspective of firstand second-order uncertainty and new measures are introduced. We conclude that the concepts of uncertainty and informativeness needs to be qualified if used in a second-order probability context and suggest that from a certain point of view information can not be minimized, just shifted from one level to another.