## Monday, August 5, 2013

### Types of Probabilities according to Keynes

A simple list of types of probabilities according to Keynes’s Treatise on Probability (although with some modern terminology):
(1) strict mathematical/physical probabilities, either a priori or relative frequency probabilities, which Keynes called “numerical” probabilities in situations of finite and mutually exclusive outcomes where the “principle of indifference” is applicable. The laws of the probability calculus apply to these probabilities, which are linear and have additive, precise values (Brady and Arthmar 2012: 80);

(2) non-numerical probabilities, not classifiable into category (1) above, that could be defined into terms of approximate intervals. These could be mathematically represented with imprecise, interval estimates (apparently called “approximation” by Keynes), the first explicit such interval estimate, lower-upper bound model of probability, developed from George Boole’s calculus in The Laws of Thought (1854) (Brady and Arthmar 2012).

These “interval” probabilities are non-linear and non-additive, and so they do not follow the laws of the probability calculus;

(3) non-numerical probabilities that can be ranked in an ordinal way (O’Donnell 2013: 128);

(4) non-numerical probabilities which cannot be ranked ordinally (O’Donnell 2013: 128).
Class (1) represents aleatory probabilities.

I assume classes (2), (3) and (4) are generally epistemic probabilities.

BIBLIOGRAPHY
Brady, Michael Emmett and Rogério Arthmar. 2012. “Keynes, Boole and the Interval Approach to Probability,” History of Economic Ideas 20.3: 65–84.

O’Donnell, R. 2013. “Two Post Keynesian Approaches to Uncertainty and Irreducible Uncertainty,” in G. C. Harcourt and Peter Kriesler (eds.). The Oxford Handbook of Post-Keynesian Economics, Volume 2. Critiques and Methodology. Oxford University Press, Oxford and New York. 124–142.