Keynes’s Theory, Based on an Imprecise, Interval Valued Approach to Probability, Rejected Ramsey’s Emphasis on the Importance of the Use of Mathematical Expectations in Decision Theory

Abstract

Keynes spent chapter 12 of the General Theory emphasizing two major points that were extremely important in long run decision making, confidence and expectations. Keynes saw that the technical analysis of the role of confidence in decision making had been overlooked in economics. Keynes corrected this lacuna in the General Theory. Confidence was defined as a function of Keynes’s evidential weight of the argument, V, where V=V (a/h) =w,0≤w≤1,just as the term “very uncertain”, used three times on p.148 of the General Theory, was defined as a function of a slight amount of information, a definition that is identical to Keynes’s definition of “very uncertain” on p.310 of his A Treatise on Probability. w equaled the degree of the completeness of the relevant information upon which the probabilities were based. Keynes’s definition of V can be found on p.315 of his A Treatise on Probability in chapter 26, titled “The application of probability to conduct”. His discussion of the completeness of the evidence can be found on pp.313-315.

The second major point was Keynes’s completely overlooked discussion of the reasonable calculation of probabilities, based on approximate and inexact measures like interval valued probability and his decision weight, c, which he called a conventional coefficient of weight and risk, c, versus the unreasonable calculation of probabilities based on strict or exact mathematical expectations calculations as advocated by Frank Ramsey. The heart of Ramsey’s theory is a reliance on betting quotients and mathematical expectations based on precise probability.