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

#### 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.

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