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# Bruno de Finetti

Bruno de Finetti (1906 - 1985) was an Italian probabilist and statistician, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ses lois logiques, ses sources subjectives," Annales de l'Institute Henri Poincaré, 7, 1-68, which discussed probability founded on the coherence of betting odds and the consequences of exchangeability.

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.

## Bibliography

### De Finetti in English

(The following are translations of works originally published in Italian or French.)
• "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in Erkenntnis, volume 31 September 1989. The entire double issue is devoted to de Finetti's philosophy of probability.
• "Foresight: its Logical Laws, Its Subjective Sources," (translation of 1937 article) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964.
• Theory of Probabilty, (translation of 1970 book) 2 volumes, New York: Wiley, 1974-5.

### Discussions

• "D. V. Lindley (1986) Bruno de Finetti, 1906-1985, (Obituary)" Journal of the Royal Statistical Society, Series A, 149, p. 252.
(The following books have a chapter on de Finetti and references to further literature.)
• Jan von Plato Creating Modern Probability Theory, Cambridge: Cambridge University Press. 1994
• Donald Gillies Philosophical Theories of Probability, London: Routledge, 2000.