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.