Using Keynes’s Non-Probabilistic Coefficient of Evidential Weight, [2w/(1+w)], to Analyze Knightian Uninsurable Uncertainties, Scenario Analysis and Entrepreneurship Studies

Michael Emmett Brady

Abstract


Knight’s third category ,”estimates “,requires  a non probabilistic ,decision  weight approach that he was unable to work out due to his inability to apply the necessary mathematical structure .However,Knight made it very clear that it would have   the same ratio  form as a probability(a/b) ,but would not be  a probability.Knight substituted a heuristic  analysis of urn ball models on pp.218-224 in order to operationalize his approach  for applications concerning his uninsurable uncertainties. Knight’s category of uninsurable uncertainties was not measurable by precise probabilities .However,it could be partially measured by his third category ,”estimates” . This conclusion follows  because Knight made it clear that his “estimates “ category had nothing to do with subjective probability. Knight’s first two categories are classical probability ,based on the Principle of Indifference and statistical frequencies, which is the frequentist approach. This leaves only two other approaches to probability left for consideration - the Popper propensity approach and the logical approach of Boole and Keynes. Knight could not have been talking about Popperian propensities since this theory was put forth only  in the 1957-58 time period. Knight could not be talking about logical probabilities  because he did not have the mathematical and statistical training to follow Boole and/or Keynes.

Knight’s “estimates “,the estimate of the confidence a business man has in his estimate of a probability ,is easily described and defined as being equal to Keynes’s weight coefficient ,2w/(1+w).Thus ,Knight’s (a/b) equals Keynes’s [2w/(1+w].

 

Knight was  very clear in his following two combined statements, which have been overlooked and/or misstated for 100 years:

 

This form of probability is involved in the greatest logical difficulties of all, and

no very satisfactory discussion of it can be given, but its distinction from the

other types must be emphasized and some of its complicated relations

indicated The confusion arises from the fact that we do estimate the value or

validity or dependability of our opinions and estimates, and such an estimate has

the same form as a probability judgment; it is a ratio, expressed by a proper

fraction. 

But in fact, it appears to be meaningless and fatally misleading to speak of the

probability, in an objective sense, that a judgment is correct. As there is little

hope of breaking away from well-established linguistic usage, even when

vicious, we propose to call the value of estimates a third type of probability

judgment,

insisting on its differences from the other types rather than its similarity to them.

It is this third type of probability or uncertainty which has been neglected in

economic theory, and which we propose to put in its rightful place.”(Knight,1921,pp.225,231;italics  added).

 

The only possible  five approaches to probability -classical, frequentist ,logical ,propensity and subjective - were discussed above .It is impossible to fit Knight’s “categories “ into any extant theory of probability simply because it is not a probability, but a decision weight. Knight simply lacked the knowledge and mathematical skill set to do what Keynes was able to do-create  a decision weight approach incorporating both probability and weight.

 

 


Full Text:

PDF

References


Arthmar, Rogério and Brady, Michael Emmett.(2018) .Boole, Ramsey and the Keynes-Townshend exchanges on subjective probability. Journal of Economic Thought and Policy,vol.18,no.2, pp. 55-74.

Arthmar, Rogério & Brady, Michael Emmett. (2017).Reply to Feduzi,Runde,andZappia. History of Economic Ideas, Vol.XXV, no.1,pp.224-233.

Arthmar, R., & Brady, M. E.( 2016). The Keynes–Knight and the de Finetti–Savage's Approaches to Probability: An Economic Interpretation. History of Economic Ideas, 24(1),pp. 105-124.

Bradley, S. (2019). Imprecise probabilities. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy.(Updated in 2019 from 2014).

Brady, Michael Emmett.(2020). A Historical Summary of How a Severe

Misinterpretation of the only Diagram in Keynes’s A Treatise on

Probability in Chapter III on Page 39 Spread to Philosophers: From G.

Meeks (1976) to S.Dow and V.Chick (2012) to S.Bradley(2019). (February

. Available at SSRN: https://ssrn.com/abstract=3532241 or

http://dx.doi.org/10.2139/ssrn.3532241.

Brady, Michael Emmett.(2020). The Claim That the Diagram on Page 39 of

Keynes’s A Treatise on Probability(1921) Represents ‘Keynes’s View of

Probability’ (S. Bradley, 2019), Has No Support: It Represents a Very

Brief Introduction to Part II of Keynes’s A Treatise on Probability On NonAdditive Probability. (January 13). Available at SSRN:

https://ssrn.com/abstract=3518231 or

http://dx.doi.org/10.2139/ssrn.3518231.

Brady, Michael Emmett.(2017). J M Keynes's Evidential Weight of the Argument, V(A/H),Which Applies to Arguments, is Different from the Weight of the Evidence, w, Which is a Measure of the Completeness of the Information, Data, Evidence, or Knowledge in the Premises, h (August 22). Available at SSRN: https://ssrn.com/abstract=3024388 or http://dx.doi.org/10.2139/ssrn.3024

Brady, Michael Emmett.(2018). The Roles of Keynes’s Logical Relations, V(a/h) =w and P(a/h) =alpha, in His Conventional Coefficient of Weight and Risk, C (April 19 ). Available at SSRN: https://ssrn.com/abstract=3165298 or http://dx.doi.org/10.2139/ssrn.3165298.

Brady, M. E. (1983). The Foundation of Keynes’ Macroeconomics: His Logical

Theory of Probability and its Application in the General Theory. U. C. Riverside,

Dissertation (July).

Brady, M .E. (1986).Reviewing the Reviewers of J.M. Keynes’s A Treatise on

Probability: How most of them got it all wrong. Unpublished paper.[Published in

as Reviewing the Reviewers of J.M. Keynes’s A Treatise on Probability:

Ignorance is Bliss. Xlibris Press; Philadelphia ,Pennsylvania].

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,pp. 357-76.

Brady, Michael Emmett.(1994). On the application of J.M. Keynes's approach to

decision making. International Studies in the Philosophy of Science,8,no.1, pp.99-

______. (2004a). J. M. Keynes’ Theory of Decision Making, Induction, and

Analogy. The Role of Interval Valued Probability in His Approach. Xlibris Corporation.(Pennsylvania;Philadelphia)

______. (2004b). Essays on John Maynard Keynes and …. Xlibris Corporation. (Pennsylvania;Philadelphia).

Brady, Michael Emmett.(2018).How J M Keynes’s Logical Theory of Probability Totally Refutes All Attacks on the concept of Probability.The Open Journal of Economics and Finance,Vol.2,pp.13

Brady, Michael Emmett.(2021a).How SIPTA overlooked Keynes’s major contributions to imprecise probability and decision making,1999-2019.International Journal of Management Research and Economics,Volume 1,no.3,pp.11-21.

Brady, Michael Emmett.(2021b).On the correction of all thirty five errors contained in Ramsey’s 1922 and 1926 reviews of Keynes’s Treatise.Journal of Management Information and Decision Science(s),Volume 24,no.6(special issue),pp.1-19.

Brady, Michael Emmett .(2022).On Knight’s Inability to Mathematically Model his third Category,”Estimates”,which Involved the Confidence a Decision Maker had in his Estimate of a Probability in Risk,Uncertainty and Profit,1921.Journal of Insurance and Financial Management,Vol. 6,no.3,pp.61-80.

Brady, Michael Emmett .(2022).Examining F. Knight’s urn ball models shows that his unmeasurable ,uninsurable uncertainties all involve partialknowledge/partial ignorance :Acturaries can use the POI to partially insure options using a lower bound. Journal of Insurance and Financial Management,Vol. 6,no.5,pp.60-80.

Feduzi, Alberto (2010). On Keynes’s conception of the weight of evidence. JournalEconomic Behavior & Organization, 76,pp. 338-351.

Gerrard,B.(2022). The Road Less Travelled: Keynes and Knight on

Probability and Uncertainty, Review of Political Economy, DOI: 10.1080/09538259.2022.2114291.

Gerrard,B.(2003).Keynesian Uncertainty:what do we know ? In Runde,J. and Mizuhara,S.(eds.),The philosophy of Keynes’s economics ,Routledge,pp.239-251.

Hishiyama,I.(1969). The Logic Of Uncertainty according to J. M.Keynes. Kyoto University Economic Review , 39,no.1,pp. 22-44.

Hishiyama,I.(2011).A Critical Reorientation of Keynes’s Economic and Philosophical Thoughts. In Silva Brandolini and R. Scazzieri, (eds.),Fundamental Uncertainty: Rationality and Plausible Reasoning. Palgrave Macmillan;London,pp.232-271

Keynes, J. M.(1997,[1936]).The General Theory of Employment, Interest and Money. Prometheus Books; New York.

Keynes, J. M. (1971–79). The Collected Writings of John Maynard Keynes, vols. 1–30. London; Macmillan.

Langlois, Richard N. and Cosgel,Metin M.(1993).Frank Knight on risk,uncertainty and the firm:a new interpretation. Economic Inquiry,Vol. XXXI,( July),pp.456-466.

LeRoy, Stephen F., and Larry D. Singell, Jr. (1987).Knight on Risk and Uncertainty.Journal of Political Economy,( April),pp.394-406

Packard, Mark D., Bylund, Per L. and Clark, Brent B.(2021). Keynes and Knight on Uncertainty: Peas in a Pod or Chalk and Cheese? Cambridge Journal of Economics. Volume 45, Issue 5,( September) , pp.1099–112 .

Rapp,D. J. and Olbrich,M. (2020). On entrepreneurial decision logics under conditions of uncertainty: an attempt to advance the current debate .Journal of Innovation and Entrepreneurship (2020),Vol, 9:21 (https://doi.org/10.1186/s13731-020-00131-7).

Rivot, Sylvie. "Reading Keynes’s policy papers through the prism of his Treatise on Probability: information, expectations and revision of probabilities in economic policy". Journal of the History of Economic Thought (forthcoming). Preprint at SocArXiv, osf.io/preprints/socarxiv.

Rizzo, Mario J. and Dold, Malte.(2021).Knightian uncertainty: through a

Jamesian window. Cambridge Journal of Economics. Volume 45, Issue 5,(

September) 2021, pp. 967–988 .

Runde,J.(1990).Keynesian Uncertainty and the Weight of Arguments.

Economics and Philosophy,6,pp.275-292.

Runde, Jochen (1994). Keynes after Ramsey:In Defence of A treatise on Probability.Studies in the History and Philosophy of Science,Vol.25,no.1,pp.97-121.

Skidelsky, R. 1992. John Maynard Keynes: The Economists as Savior, 1920–1937, New York, Viking.

Vercelli, A.(2011).Weight of Argument and Economic decisions.In Fundamental Uncertainty,eds by Brandolini,S and Scazzieri,R.,England,Palgrave Macmillan,pp.151-170.

Vercelli , A.(2013). Weight of Argument and liquidity preference: Keynes after Savage and Choquet. Department of Political Economy and Statistics University of Siena,pp.1-21.

Vercelli,A.(2016). Weight of Argument and liquidity preference: Maynard Keynes and Victoria Chick. Department of Political Economy and Statistics University of Siena,pp.1-19.

Vercelli,A.(2018). Weight of Argument and liquidity preference: Maynard Keynes and Victoria Chick.In The General Theory and Keynes for the 21st Century. S DowJ.Jesperson, and G. Tily,(eds.).Edward Elgar,London,pp.84-97.

Weatherson, B. (2002). Keynes, uncertainty, and interest rates. Cambridge Journal of Economics, 26, pp.47–62.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Michael Emmett Brady

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.