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Indeterminate versus Imprecise Interval Probabilities: The Keynes-Knight and the De Finetti-Savage Approaches

The operational definitions of uncertainty used by John M. Keynes and Frank H. Knight are based on missing information that will not be available to the decision maker at any time. The founder of this approach is George Boole. This leads to indeterminate interval probabilities. The definition of uncertainty proposed by Bruno de Finetti and Leonard J. Savage is significantly different from the one advanced by Keynes and Knight. Uncertainty, for de Finetti and Savage, can only exist in the initial conditions of an experiment or study due to measurement error or a lack of data available at the beginning of a study. Imprecise interval probabilities will always eventually result in precise probabilities due to Bayesian conditionalization. Recent studies, such as the papers by Feduzi, Runde and Zappia (2012, 2014), seem to have overlooked this particular aspect of de Finetti and Savage’s 1962 paper ‘Sul Modo di Scegliere le Probabilita Iniziali’. This particular work is cited by the said scholars as supporting their claim that there are similarities between the de Finetti-Savage conception of uncertainty and the Keynes-Knight approach. This claim, however, loses much of its appeal once it is realized that the discussion of de Finetti and Savage involves only the initial probabilities.