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Inside critics of the Bayesian mainstream in economics: letters to Leonard Jimmie Savage
Carlo Zappia

Last modified: 2016-06-11

Abstract


The paper provides a preliminary scrutiny of archival material concerning the reception of Leonard Savage’s Foundation of Statistics among fellow decision theorists. Specifically, the paper concentrates on the criticism put forward by Daniel Ellsberg and William Fellner in a symposium on decision-making under uncertainty hosted in the Quarterly Journal of Economics in 1961. Both Ellsberg and Fellner, echoing a previous work by Irvin J. Good, suggested that a relevant mis-representation of uncertainty was implicit in Savage’s assumption that a single probability prior can represent the degrees of belief of decision-makers. Although the episode is well-known, due to the introduction of the notion of ambiguity by Ellsberg in his paper, Savage’s reaction to critics has never been examined. Indeed this is not surprising since in his published writings Savage never really engaged with the issue, his interest in the topic apparently being very limited. However, mainly after the statistician Cedric Smith suggested an operational version of the criticism, he seemed to devote attention to the issue, sharing his concern about interval-valued probability priors with Bruno de Finetti, in an appendix to a long joint paper written in Italian in 1962.

Through an examination of letters from Savage’s private exchange with Ellsberg, Fellner, Good and Smith in the early 1960s the paper shows how Savage reacted to the generalization of the Bayesian viewpoint that was advocated by his correspondents. Although all of them were supporters of a Bayesian viewpoint to probability and decision-making, they could not understand Savage’s insistence on the strict version suggested to him by de Finetti. Apparently, Savage did not change his mind on the issue, but the paper suggests that his viewpoint, which he shared with de Finetti, was more nuanced than admitted in published works.


Keywords


probability, uncertainty, Bayesian decision-making

Full Text: Paper Zappia