Since the early days of probability theory, there has been a distinction between probabilities that are given, as in a game of chance, and probabilities that are not given, but reflect a subjective degree of belief; Hacking (1975) and Shafer (1978) offer historical surveys. In economics, Knight (1921) is typically credited with the distinction between situations of "risk" and of "uncertainty." In his formulation, "risk" designates situations in which probabilities are known, or knowable in the sense that they can be estimated from past data and calculated using the laws of probability. By contrast, "uncertainty" refers to situations in which probabilities are neither known, nor can they be deduced, calculated, or estimated in an objective way. The Bayesian approach minimizes the importance of this distinction by introducing the notion of "subjective probability." According to this approach, when objective probabilities are not known, they can be replaced by subjective ones, so that problems of decision under uncertainty are reduced to problems of decision under risk.
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