The Role of Subjective Probability and Utility in Decision-Making

Abstract

Although many philosophers and statisticians believe that only an objectivistic theory of probability can have serious application in the sciences, there is a growing number of physicists and statisticians, if not philosophers, who advocate a subjective theory of probability. The increasing advocacy of subjective probability is surely due to the increasing awareness that the foundations of statistics are most properly constructed on the basis of a general theory of decision-making. In a given decision situation subjective elements seem to enter in three ways: (i) in the determination of a utility function (or its negative, a loss function) on the set of possible consequences, the actual consequence being determined by the true state of nature and the decision taken; (ii) in the determination of an a priori probability distribution on the states of nature; (iii) in the determination of other probability distributions in the decision situation.