The Beginnings of Axiomatic Subjective Probability

Abstract

We study the origins of the axiomatization of subjective probabilities. Starting with the problem of how to measure subjective probabilities, our main goal was to search for the first explicit uses of the definition of subjective probability using betting odds or ratios, i.e., using the Dutch book argument, as it is presently known. We have found two authors prior to Ramsey (The foundations of mathematics and other logical essays. Routledge & Kegan Paul, 1931, [43]) and de Finetti (Fund Math 17:298–329, 1931, [20]) that used the mentioned definition: Emile Borel, in an article of 1924, and Jean-Baptiste Estienne, a French army officer, in a series of four articles published in 1903 and 1904. We tried to identify, in the references given by Borel and Estienne, inspirations common to Ramsey and de Finetti in order to determine, in the literature on the probability of the beginning of the last century, at least some elements that point to specific events that lead to the referred axiomatization. To the best of our knowledge, the genesis of the axiomatic approach in the subjective school was not traced yet, and this untold history can give us a better understanding of recent developments and help us, as applied scientists, in future works.