Paradox? What Paradox? On a Brief Correspondence Between Leonard Savage and Karl Popper

This paper documents an exchange between Leonard Savage, founder of the subjective probability approach to decision-making, and Karl Popper, advocate of the so-called propensity approach to probability, of which there is no knowledge in the literature on probability theory. Early in 1958, just after being informally tested by Daniel Ellsberg with a test of consistency in decision-making processes that originated the so-called Ellsberg Paradox, Savage was made aware that a similar argument had been put forward by Popper. Popper found it paradoxical that two apparently similar events should be attributed the same subjective probability even though evidence supporting judgement in one case was different than in the other case. On this grounds Popper rejected the subjective probability approach. Inspection of the 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. Savage wrote to Popper denying that his criticism had paradoxical content and a brief exchange followed. The paper shows that while Savage was unconvinced by Popper’s argument he was not hostile to an axiomatically founded generalization of his theory. This draft of the paper, preliminary to that accepted for publication in RHETM, was presented at the STOREP Meeting in Genova (June 2018) and at the THETS Meeting in Oxford (August 2018). Comments by Marcello Basili, George Bent, Jack Birner, Alberto Feduzi, Nicola Giocoli, Harro Maas, Aldo Montesano, Jochen Runde are gratefully acknowledged.