On J M Keynes’s Rejection of the Moscow School of Probability’s Limiting Frequency Approach to Probability and Kolmogorov’s Axiom of Additivity (Countable Additivity ): Non –Additivity was the fundamental, basic axiom upon which all of the Economics of Ke

Michael Emmett Brady
DOI: http://dx.doi.org/10.19085/journal.sijmd021102

Abstract

J M Keynes was an acknowledged, world renown, and internationally recognized expert in probability and statistics in the 1930’s based on his A Treatise on Probability (1921). . Keynes had been selected by statistics journals to serve as a referee during the 1930’s. It is, therefore, no surprise that he was selected as the referee by the League of Nations to review Jan Tinbergen’s work on business cycles that used an econometrics approach based on The Law of Large Numbers, the Central Limit Theorem, and the Gaussian (Normal) Distribution .The fundamental axiom used by Tinbergen was additivity . Kolmogorov and the Moscow School of Probability’s main innovation was to go from the axiom of additivity to the axiom of countable additivity. However, Keynes rejected additivity except in the special case that the weight of the evidence, w, which measured the relative completeness of the evidence ,defined on the closed unit interval [0,1],equaled 1 , approached 1,or approximated 1. Keynes also accepted goodness of fit tests, such as the Lexis –Q test, and exploratory data analysis as evidence that could be used to support using a particular probability distribution.

Keywords

Moscow School of Probability; Kolmogorov’s Axiom of Additivity; Economics of Keynes

Full Text:

PDF

References

Anily, S. and Federgruen, A. (1987). "Ergodicity in Parametric Nonstationary Markov Chains: An Application to Simulated Annealing Methods." Operations Research, 1987, 35, No.6, (November-December) 867-874.

http://dx.doi.org/10.1287/opre.35.6.867

Boole, George. 1854. An Investigation of the Laws of Thought on Which are founded the Mathematical Theories of Logic and Probability. New York: Dover Publications, 1954

Brady, Michael Emmett. (2011).A Comparison-Contrast of Adam Smith, JM Keynes and Jeremy Bentham on Probability, Risk, Uncertainty, Optimism-Pessimism and Decision Making with Applications Concerning Banking, Insurance and Speculation. International Journal of Applied Economics and Econometrics, Volume 19, No.4, October -December, pp. 86-111.

Brady, Michael Emmett. (2015).Adam Smith's Theory of Probability and the Roles of Risk and Uncertainty in Economic Decision Making. International Journal of Applied Economics and Econometrics, Vol. 23, no.1,2015.

Brady, Michael E.(2015) .Paul Davidson, the Post Keynesians, and the Inductive Fallacy of Conditional A priorism (Long Runism) -Why the Ergodic-Non Ergodic distinction is meaningless and erroneous for ALL Decision Makers. Available at SSRN.

Brady, Michael E. 1993. "J.M. Keynes' theoretical approach to decision making under condition of risk and uncertainty." The British Journal for the Philosophy of Science 44: 357-76.

http://dx.doi.org/10.1093/bjps/44.2.357

Brady, Michael E. 2002. "J.M. Keynes's Theory and Preference Reversals." International Journal of Applied Economics and Econometrics 1: 301-08.

Brady, Michael E. 2004A. J.M. Keynes' Theory of Decision Making, Induction, and Analogy. The Role of Interval Valued Probability in His Approach. Bloomington: Xlibris Corporation.

Brady, Michael E. 2004B. Essays on John Maynard Keynes and …. Bloomington: Xlibris Corporation.

Brady, Michael E., Arthmar, Rogério. 2012. "Keynes, Boole and the interval approach to probability." History of Economic Ideas, XX (3): 65-84.

Brady, Michael Emmett. (2012). Keynes, Mathematics and Probability: A Reappraisal. International Journal of Applied Economics and Econometrics, Volume 20, no. 2, April-June 2012, pp.324-357Broad, C.D. 1922. "A Treatise on Probability by J.M. Keynes." Mind, 31: 72–85.

Edgeworth, Francis Y. 1922. "Review of A Treatise on Probability." Journal of the Royal Statistical Society 85: 107-13.

http://dx.doi.org/10.2307/2340524

Edgeworth, Francis Y. 1922. "The Philosophy of Chance." Mind 31: 157-285.

http://dx.doi.org/10.1093/mind/xxxi.123.257

Davidson, Paul. (1982-83).Rational Expectations: A fallacious foundation for studying crucial decision-making processes, Journal of Post Keynesian Economics, Vol. 5, No.2, pp. 182-198.

http://dx.doi.org/10.1080/01603477.1982.11489355

Davidson, Paul. (n.d.).SAMUELSON AND THE KEYNES/POST KEYNESIAN REVOLUTION: THE EVIDENCE SHOWING WHO KILLED COCK ROBIN, p.18.

Davidson Paul. (2005). STRONG UNCERTAINTY AND HOW TO COPE WITH IT TO IMPROVE ACTION AND CAPACITY. EAEPE Conference. Bremen, Germany. November 11, 2005.

Davidson, Paul. (2008). Post World War II politics and Keynes's aborted revolutionary economic theory.,Economia e Sociedade, Campinas, v. 17, Número especial, p. 549-568, Dec. 2008 .

http://dx.doi.org/10.1590/S0104-06182008000400002

Davidson, Paul. (2009).Can future systemic financial risks be quantified? Ergodic vs. Nonergodic stochastic processes. Brazilian Journal of Political Economy, vol. 29, nº 4 (116), pp. 324-340, October-December/2009

Davidson, Paul. (2012). "Is economics a science? Should economics be rigorous? ", real-world economics review, issue no. 59, 12 March 2012, pp. 58-66,.

Franklin, Johanna and Towsner, Henry. (2013).Randomness and Non-Ergodic Systems. NSF grant DMS-1340666.

Johnson, Jean and Isaacson, Dean. (1988).Conditions for Strong Ergodicity Using Intensity matrices. Journal of Applied Probability, Vol. 25, No.1 (March 1988), pp.34-42.

http://dx.doi.org/10.2307/3214231

Keynes, John Maynard. (1921). a Treatise on Probability. England: Macmillan.

Keynes, J. M. (1921). A Treatise on Probability. The Collected Writings of John Maynard Keynes (CWJMK) vol. VIII. London: Macmillan, 1973

Keynes, John Maynard. (1936).The General Theory of Employment, Interest and Money. New York: Harcourt, Brace and World.

Madsen, R.W. and Isaacson, D.L. (1973) .Strongly Ergodic Behavior for Non Stationary Markov Processes." Annals of Probability, 1973, 1(2), 329-335.

http://dx.doi.org/10.1214/aop/1176996986

Mukhamedov, F. (2012).On L 1 –Weak Ergodicity of Non homogeneous Discrete Processes and Its Applications.

Shinkai, S. and Aizawa, Y. "The Lempel-Ziv Complexity of Non-Stationary Chaos in Infinite Ergodic Cases." Progress of Theoretical Physics, 2006, 116(3), 503-515.

http://dx.doi.org/10.1143/PTP.116.503

Smith, Adam. (1776).The Wealth of Nations. Modern (Cannan) Library Edition with the foreword by Max Lerner. New York, New York .

Smith, Adam. (1759). the Theory of Moral Sentiments. Sixth edition, 1790. Gutenberg Publishers (2011).

http://dx.doi.org/10.1093/oseo/instance.00042831

Be a part of worldclass research: Publish with us