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

Résumé

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.