Risk versus Uncertainty in Frank Knight’s Thought

Runde (1998) examines Frank Knight’s ideas on risk versus uncertainty.

In essence, Knight drew two distinctions, as follows:

(1) Risk
Risk involves being able to assign objective numeric probabilities, whether under a priori or relative frequency (statistical frequency) theories of probability.

(2) Uncertainty
Uncertainty is faced in situations where a person cannot assign objective numeric probabilities, because one cannot calculate such probabilities. (Runde 1998: 540).

Runde (1998) points to a subtle part of Knight’s thought on probability: Knight considered statistical probability (as obtained by relative frequencies) to be an intermediate type of probability between a priori probability and uncertainty (Runde 1998: 541). That is, according to Knight, there was a continuum of probability situations in Knight’s way of thinking (Runde 1998: 541).

But in the calculation of statistical probabilities, often the individual events or things grouped into a given reference class of events are far less homogenous than, say, the throws of a fair game of dice (Runde 1998: 541).

The problem, as Runde sees it, is that elsewhere Knight acknowledges a fundamental epistemological distinction between (1) a priori and (2) statistical (or relative frequency) probability. The first is a priori, but the latter is a posteriori (Runde 1998: 542).

The crucial point, then, is that the probabilities obtained on the basis of statistical probability are in a different epistemological category from the certainty of a priori probability: the relative frequency probabilities are a posteriori and the certainty that is found in a priori probabilities, such as in abstract and fair dice throws or roulette games, is absent (Runde 1998: 541).

In view of this, according to Runde, Knight’s “continuum” view of probability situations is severely undermined and must be rejected (Runde 1998: 542, 544).

The precondition for the calculation of an a priori probability is that we have a finite, exhaustive and exclusive number of outcomes which are all equiprobable, but one cannot necessarily do this with statistical (or relative frequency) probabilities, which remain in a different epistemological category.

Further Reading
“The Epistemic Types of Probability,” May 17, 2014.

Probability Theory 101.

BIBLIOGRAPHY
Runde, Jochen. 1998. “Clarifying Frank Knight’s Discussion of the Meaning of Risk and Uncertainty,” Cambridge Journal of Economics 22.5: 539–546.

A Note on Mises and the Concept of Uncertainty

A rather good question is posed here about Mises and the concept of uncertainty in the Knightian sense.

The earliest work by Ludwig von Mises on uncertainty that I can think of is in the English edition of Human Action (1949) in Chapter VI, long after Keynes had published “The General Theory of Employment,” Quarterly Journal of Economics 51 (1937): 209–223.

Both Keynes and Frank Knight came to their views on uncertainty largely independently without any influence from Mises, as far as I am aware.

Frank H. Knight’s Risk, Uncertainty and Profit (Houghton Mifflin, Boston) was published in 1921. I see no evidence Knight was influenced by Mises. Curiously, in the introduction to the scholar’s edition of Human Action, we have this account of Mises’s inspiration for the chapter on uncertainty:

“Several commentators have noted the similarity of Mises’s distinction between class probability and case probability and that between risk and uncertainty introduced by Knight in Risk, Uncertainty and Profit in 1921.

Yet, it does not appear that Mises was influenced by Knight in this regard. Mises had been long familiar with Knight’s work, and had already made reference to Risk, Uncertainty and Profit in Nationalökonomie in conjunction with his discussion of profit and uncertainty.

Rather, it appears more likely that Mises’s Chapter VI was stimulated and influenced by his younger brother, Richard von Mises (1883–1953). A professor of aerodynamics and applied mathematics at Harvard University, Richard von Mises’s most outstanding theoretical achievement was his contribution, from 1919 onward, to the frequency theory of probability. In principle, Ludwig accepted Richard’s frequency interpretation of probability, but Ludwig provided a new definition of randomness, and thus significantly improved on Richard’s theory. (Mises 1998: xvi).

But the idea that Mises was not influenced by Knight in regard to his chapter on uncertainty rings hollow to me. If Mises had been “long familiar with Knight’s work” and actually cited it in Nationalökonomie (first published in Geneva in 1940), then the view that there was some influence from Knight on Mises’s thinking on uncertainty seems plausible.


BIBLIOGRAPHY

Knight, F. H. 1921. Risk, Uncertainty and Profit, Houghton Mifflin, Boston.

Mises, L. 1940. Nationalökonomie, Theorie des Handelns und Wirtschaftens, Éditions Union, Geneva.

Mises, L. 1998. Human Action: A Treatise on Economics. The Scholar’s Edition, Mises Institute, Auburn, Ala.

Keynes, J. M. “The General Theory of Employment,” Quarterly Journal of Economics 51 (1937): 209–223.