Analysis of Decisions with Incomplete Knowledge of Probabilities

This paper discusses the application of personalistic decision theory in a typical setting of decision making under uncertainty. The criterion for choice of strategy is maximization of expected utility. In this setting it is often difficult to obtain very precise measurements of the decision maker's probabilities on the states of nature. We therefore pay particular attention to several “imprecise” measures of probability, including sets of inequalities and bounds, and see how this information may be used in trying to determine an ordering or partial ordering of the expected utilities of the alternative strategies. At the end of the paper we note how, in practice, one may try to obtain the measures of probability presented herein.