De Finetti proposed a thought experiment along the following lines: You must set the price of a promise to pay $1 if there was life on Mars 1 billion years ago, and $0 if there was not, and tomorrow the answer will be revealed. You know that your opponent will be able to choose either to buy such a promise from you at the price you have set, or require you to buy such a promise from your opponent, still at the same price. In other words: you set the odds, but your opponent decides which side of the bet will be yours. The price you set is the "operational subjective probability" that you assign to the proposition on which you are betting. This price has to obey the probability axioms if you are not to face certain loss, as you would if you set a price above $1 (or a negative price). By considering bets on more than one event de Finetti could justify additivity. Prices, or equivalently odds, that do not expose you to certain loss are called coherent. See coherence (philosophical gambling strategy).
De Finetti is also noted for de Finetti's theorem on exchangeable sequences of random variables. De Finetti was not the first to study exchangeability but he put the subject on the map. He started publishing on exchangeability in the late 1920s but the 1937 article is his most famous treatment.
De Finetti studied mathematics at Milan University. After graduation, he did not pursue an academic career but worked as an actuary and a statistician. He published extensively (17 papers in 1930 alone, according to Lindley) and acquired an international reputation in the small world of probability mathematicians. He won a chair in Financial Mathematics at Trieste University (1939). In 1954 he moved to the University of Rome, first to another chair in Financial Mathematics and then, from 1961 to 1976, one in the Calculus of Probabilities. De Finetti developed his ideas on subjective probability in the 1920s independently of Frank P. Ramsey. He only became known in the Anglo-American statistical world in the 1950s when L. J. Savage, who had independently adopted subjectivism, drew him into it.
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Bibliography
De Finetti in English
(The following are translations of works originally published in Italian or French.)
Discussions
(The following books have a chapter on de Finetti and references to further literature.)
External links
(De Finetti's views are discussed in Section 3.5 of the article)