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Probability and Uncertainty

The Treatise on Probability must be interpreted in the light of the culture of Cambridge at the time: the tradition of John Stuart Mill’s logical inducti- vism (upheld also by Maynard’s father, who in his 1891 book attempted an eclectic synthesis between it and German historicism). In the same years that saw Keynes at work on probability theory, Bertrand Russell (1872-1970) and Alfred Whitehead (1861-1947) went ahead on the project of deducing mathematics from purely logical premises, publishing the Principia mathematica (1910-13).

Keynes’s ambition was to build a general theory of knowledge and rational behaviour, with respect to which the cases ofperfect certainty and total ignorance are the extremes. For this reason Keynes rejected the frequentist interpretation of probability, applicable only to that class of phenomena for which we can assume the possibility of an infinite series of repetitions under unchanged conditions. He proposed, instead, a rationalist approach, centred on the degree of confidence that it is reasonable to have about a certain event, given the state of knowledge. To economists, the importance of this view lies in the fact that it deals with the problem of rational behaviour in a context in which the subject is devoid of certainties. Rational behaviour is then connected to subjective evaluations based on experience and personal intuitions; probability calculus is the technique by which these evaluations are screened.

Keynes distinguished between the proposition that expresses the probability of a given event and the confidence that one can have in such an evaluation, named ‘weight of the argument’. When relevant empirical evidence - understood as the set of information directly or indirectly useful for our assessment of the event - increases, then the weight of the argument increases, while the probability attributed to the event may increase or diminish or remain unchanged. Moreover Keynes rejected the idea that it was always possible to attribute a numerical value to the probability of events: in some instances we can do it (for instance, in the game of dice or mortality tables: in general, in all cases of actuarial risk); in other instances we can express non-quantitative opinions on partial ranking of events; in yet other instances the knowledge basis is insufficient for us to formulate even relative judgments of this kind. When confronted with events belonging to the second or third class, it may be rational to rely on conventional forms of behaviour, conforming to or possibly anticipating the behaviour of the majority.[1]

  • [1] Thus, Keynes’s approach should be kept distinct from the subjective one developed a fewyears later by Ramsey (1931), DeFinetti (1930,1931,1937) and Savage (1954), who sawprobabilities in terms of subjective evaluations expressed through bets and thus generallyquantifiable. Moreover, the Keynesian notion of uncertainty, which played a crucial rolein his theory of money, income and employment, has rather more substance than both thedistinction drawn by Knight (1921) between probabilistic risk and uncertainty andMenger’s treatment (1871) of the limits of economic agents’ knowledge. Cf. Roncaglia,2009a.
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