Dopo Von Neumann e Morgenstern: il dibattito dagli Anni Quaranta agli Anni Cinquanta

Favero, Gino ; Modesti, Paola

La Matematica nella società e nella cultura, Série 1, Tome 6 (2013) no. 2, pp. 263-298.

Riassunto (VO)

A metà degli Anni Quaranta si apre un dibattito estremamente fertile attorno alla Teoria delle decisioni. Ciò è dovuto, da un lato, alla grande portata innovativa del lavoro di von Neumann e Morgenstern, apparso nel 1944 e destinato ad assumere ben presto il ruolo di paradigma, e, dall'altro, ai tempi ormai scientificamente e culturalmente maturi per l'``esplosione'' della teoria in ambito aleatorio. Nel maggio del 1952 si tiene a Parigi il convegno Colloque sur les Fondaments et Applications de la Theorie du Risk en Econométrie, a cui partecipano i più prestigiosi matematici economici dell'epoca (da de Finetti a Savage, da Arrow a Samuelson, da Friedman ad Allais), nel quale sono presentate, seppur in embrione, le critiche e le proposte che in seguito contribuiranno in misura significativa allo sviluppo della teoria. Le numerose perplessità emerse nel corso degli anni sembravano tuttavia destinate a restare inascoltate e, in effetti, così fu per oltre trent'anni. Le frequenti violazioni sperimentali degli assiomi ed il dibattito che si era andato sviluppando hanno, però, lanciato una sfida alla Teoria delle decisioni ed hanno preparato il terreno per i nuovi potenti modelli che saranno proposti a partire dalla fine degli Anni Ottanta. Questo lavoro offre una rassegna dei principali temi del dibattito, facendo parlare direttamente molti dei protagonisti. Ne esce un quadro vivacissimo e, per certi versi, ancora attuale.

Abstract

In mid 1940s a very lively debate arises around Decision Theory. This is due, on one hand, to the strong innovation carried by von Neumann and Morgenstern's work, appeared in 1944 and bound to become a cornerstone shortly thereafter, and, on the other hand, to times being scientifically and culturally mature for that Theory to ``explode'' in a stochastic setting. In May, 1952, the convention Colloque sur les Fondaments et Applications de la Theorie du Risk en Econométrie is held in Paris, where the most glamorous mathematicians of the time (from de Finetti to Savage, from Arrow to Samuelson, from Friedman to Allais) gather and introduce, although still in an embryo stage, critics and proposals that will significantly contribute to the development of the Theory. In spite of that, the several perplexities, that popped out in the years, appeared bound to be unheeded, and actually were for more than thirty years. Frequent experimental violations of the axioms, and the debate that started developing afterwards, set nevertheless a challenge for Decision Theory and prepared the ground to the new and powerful models proposed from the 1980s on. This work offers a survey of the main topics in the debate through the words of the protagonists themselves: the result is a very lively, and mostly still topical, picture.

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