Bruno de Finetti

Life

De Finetti was born in Innsbruck, Austria and studied mathematics at Politecnico di Milano. He graduated in 1927 writing his thesis under the supervision of Giulio Vivanti. After graduation, he worked as an actuary and a statistician at Istituto Nazionale di Statistica (National Institute of Statistics) in Rome and, from 1931, the Trieste insurance company Assicurazioni Generali.

He published extensively (17 papers in 1930 alone, according to Lindley) and acquired an international reputation in the small world of probability mathematicians. He taught mathematical analysis in Padua and then won a chair in Financial Mathematics at Trieste University (1939). In 1954 he moved to the Sapienza 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. Still, according to the preface of his Theory of Probability, he drew on ideas of Harold Jeffreys, I. J. Good and B.O. Koopman. 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; another great champion was Dennis Lindley. De Finetti died in Rome.

Work

De Finetti emphasized a predictive inference approach to statistics; he proposed a thought experiment along the following lines (described in greater detail at coherence (philosophical gambling strategy)): 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 through a Dutch book are called coherent.

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 brought the subject to greater visibility. He started publishing on exchangeability in the late 1920s but the 1937 article is his most famous treatment.

In 1929, de Finetti introduced the concept of infinitely divisible probability distributions.

He also introduced de Finetti diagrams for graphing genotype frequencies.

The 1974 English translation of his book is credited with reviving interest in predictive inference in the Anglophone world, and bringing the idea of exchangeability to its attention.

In 1961 he was elected as a Fellow of the American Statistical Association. The de Finetti Award, presented annually by the European Association for Decision Making, is named after him.

Political philosophy

De Finetti's 1931 paper "Probabilismo" closes with a remarkable pean to Fascism, connecting it to his philosophy of probability.

"But where my spirit rebelled most ferociously and clashed against the concept of "absolute truth" was in the political field, and I could not say what part, surely very great, this sense of impatient revolt must have had in the development of my ideas. To be confronted by papier-mâché idols and a miserable political class that would have preferred Italy in ruins rather than failing (sacrilege!) to render due homage! Those delicious absolute truths that stuffed the demo-liberal brains! That impeccable rational mechanics of the perfect civilian regime of the peoples, conforming to the rights of man and various other immortal principles! October of '22! It seemed to me I could see them, these Immortal Principles, as filthy corpses in the dust. And with what conscious and ferocious voluptuousness I felt myself trampling them, marching to hymns of triumph, obscure but faithful Blackshirt."

Though writers often find it necessary or expedient to pay lip service to oppressive regimes, de Finetti's eloquence suggests some degree of sincerity, at least at the time. On the other hand, the de Finetti website[1] notes that he was politically active as an anti-militarist during the 1970s.