UNCERTAINTY ABOUT PROBABILITY - A RECONCILIATION WITH THE SUBJECTIVIST VIEWPOINT

The use of probability distributions to represent uncertainty about pr obabilities (rather than events) has long been a subject of controvers y among theorists. Many well-known theorists, such as de Finetti, have concluded that it is inherently meaningless to be uncertain about a p robability, because this appears to violate the subjectivists' assumpt ion that individuals can develop unique and precise probability judgme nts. Others have found the concept of uncertainty about probability to be both intuitively appealing and potentially useful. This paper pres ents a resolution of this question, indicating that at least one type of uncertainty about probabilities (that arising from uncertainty abou t 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) appea rs not to be consistent with the axioms of subjective probability as t hey are currently formulated. Distinguishing between these two sources of uncertainty is an important step in resolving the persistent theor etical controversy over uncertainty about probability. We also show th at uncertainty about probability will be potentially relevant to decis ion making whenever the expected value of the relevant performance mea sure is nonlinear in the probability in question.