Uncertainty about probability: a reconciliation with the subjectivist viewpoint

Abstract
The use of probability distributions to represent uncertainty about probabilities (rather than events) has long been a subject of controversy among theorists. Many have concluded that it is inherently meaningless to be uncertain about a probability, because this appears to violate the subjectivists' assumption that individuals can develop unique and precise probability judgments. Others have found the concept of uncertainty about probability to be both intuitively appealing and potentially useful. This paper presents a resolution of this question, indicating that at least one type of uncertainty about probabilities (that arising from uncertainty about the underlying events on which those probabilities are conditioned) is consistent with the subjective theory of probability. Another type of uncertainty (namely, that arising from cognitive imprecision) appears not to be consistent with the axioms of subjective probability as they are currently formulated, Distinguishing between these two sources of uncertainty is an important step in resolving the persistent theoretical controversy over uncertainty about probability. We also show that uncertainty about probability will be potentially relevant to decision-making whenever the expected value of the relevant performance measure is nonlinear in the probability in question.