Greenspan's Synthesis of the ‘Keynes-Knight’ Approach and the Ramsey-De Finetti-Savage Approach in Decision Making: A Continuum Exists Between Situations of No Knowledge and Complete Knowledge

The differences between Knight’s approach in Risk, Uncertainty and Profit (1921) and Keynes’s logical theory of probability approach in the A Treatise on Probability (1921), on the one hand, and the Ramsey-Savage-de Finetti Subjective or Bayesian approach, on the other hand, are based on the question of whether it is always possible or not to estimate a probability with a precise, exact, numerical value. Keynes and Knight argued that it is not always possible to provide a precise numerical answer to the question, “What is the probability of this outcome relative to this evidence?”, while Ramsey, de Finetti and Savage argued that it was always possible. de Finetti and Savage added a qualification regarding their views on numerical probability only in the case involving the initial conditions at the beginning of a probability assessment. Due to a lack of enough evidence in the beginning stage of a probability assessment, an imprecise estimate of probability could result. However, as time went on, more additional, sufficient evidence would result that would always lead to a precise probability estimate. Much important evidence would be missing or vague or Ambiguous (Daniel Ellsberg’s term). Keynes and Knight argued that that there would be many cases of what Keynes called indeterminate probability estimates, where additional evidence would not be sufficient to lead to a precise probability by the time a decision had to be made. It is impossible to postpone many financial, economic, and business decisions until more, relevant information has accumulated that would lead to the convergence of a imprecise probability to a precise probability at some point in the future. Thus, it is the relative strength of the evidence that determines if a numerically precise probability can be assigned. The mathematical laws of the probability calculus assume that the available evidence used is relevant and complete before a probability calculation takes place. This is a situation of strong evidence. On the other hand, if evidence is missing or not available, one is dealing with a situation of weak evidence. Greenspan cuts through the logical, epistemological, and philosophical analysis made by Keynes and Knight to arrive at a simple and direct definition of uncertainty that entails the work of Keynes and Knight.