Early in 1958, just after being informally tested by the young Daniel Ellsberg—a test of consistency in decision-making originating the so-called Ellsberg Paradox which he allegedly failed (Ellsberg 1961)—Leonard Savage was made aware by the mathematical statistician Irving J. Good that an argument similar to Ellsberg’s had just been put forward by the philosopher Karl Popper.

Popper—an advocate of an objective approach to probability in the peculiar form of the so-called propensity interpretation—suggested that he found paradoxical that two apparently similar events should be attributed the same subjective probability even though the evidence supporting judgement in one case was substantially different than in the other case. Popper referred to his case as the “paradox of ideal evidence,” recalling that similar perplexities were already pointed out by Keynes (1921) with his weight of argument, and presented the paradox as a crucial element of his rejection of a subjective approach to probability.

Inspection of the Leonard Savage Papers archived at Yale University Library makes it possible to document Savage’s reaction to Popper, of which there is no evidence in his published writings. In March 1958, presenting himself as a supporter of the subjective approach to probability, Savage wrote to Popper, denying that his criticism had paradoxical content. A brief exchange followed, but Popper seemed uninterested in detailing his argument against Savage’s position, and no proper debate followed.

The paper surveys the way Savage confronted Popper’s approach to probability and argues that Savage’s argument against Popper can be taken as evidence of his possible reaction to Ellsberg’s critique, which he never confronted publicly. It emerges that Savage was unconvinced by Ellsberg’s argument as much as Popper’s, but he did not oppose in principle to an axiomatically founded generalization of his theory, as alluded in an ensuing exchange with William Fellner, who had sided with Ellsberg in Fellner (1961).

Keywords: probability, paradoxes, Savage, Popper