Abstract

The SIPTA (Society for Imprecise Probability, Theory and Application) view of Keynes’s contributions to imprecise probability and application form a one-to-one, onto mapping from the claims of Henry E Kyburg to what is the accepted as being what Keynes’s contribution was. Thus, if one is familiar with Kyburg’s assessment of Keynes’s contributions, then one also knows what SIPTA’s views of Keynes’s contributions are. There is an extremely severe problem here, however, because Kyburg never read beyond chapter 6 in Keynes’s A Treatise on Probability. Kyburg was, therefore, ignorant about the many technical and mathematical contributions made to the theory of imprecise probability by Keynes, such as upper and lower probabilities, non-additive probabilities, sub additive probabilities, interval valued estimates, decision weights, etc., in Parts II, III, IV and V of the A Treatise on Probability. Keynes’s applications of non-additive probability appear in his analysis of uncertainty in the theory of the liquidity preference approach to the rate of interest, where uncertainty was defined as an inverse function of the evidential weight of the argument in footnote 1 on page 148 of chapter 12 of the General theory, which Keynes greatly emphasized in his correspondence with Townshend in 1937-38. Kyburg’s view of Keynes’s contribution was to argue, based on Keynes’s verbal discussions on pp.30-34 of chapter III of Keynes’s A Treatise on Probability, that Keynes had been the first to (a) define a partial order and (B) the first to argue that all probabilities were not comparable and measurable. Kyburg also acknowledged Keynes’s contribution in chapter 6 concerning the weight of the argument as it related to the Bayesian refusal to give any importance to questions dealing with the relative strength of the evidence of different probabilities, i.e., whether the evidentiary base supporting a probability estimate was composed of strong evidence or made up of weak evidence. We will conclude that this assessment of Kyburg’s is identical to the SIPTA assessment made from 1999 (Kyburg’s 1999 assessment for SIPTA) to the last SIPTA meeting in 2019 (SIPTA, 2015 as an example).

Keywords: Non-numerical probabilities, Non (sub) additive probabilities, Decision weights, Lower and upper probabilities, Imprecise probability, Inexact and approximate probabilities