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Adam Smith rejected the use of the mathematical laws of the calculus of probabilities because the basic information-data-knowledge provided in the real world of decision making did not allow a decision maker to specify precise, definite, exact, numerical probabilities or discover the probability...
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Both Smith and Keynes have very similar conceptual approaches to what probability is, how it is used and applied and the areas of application in which it can aid a decision maker. They both accept an interval approach to probability based on inequalities and bounds versus ordinal, subjectivist...
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