Prospects and Problems in Applying the Fundamental Theorem of Prevision as an Expert System: An Example of Learning About Parole Decisions

The operational subjective theory of probability and statistics recognizes Bruno de Finetti’s fundamental theorem of prevision as providing the basis for any coherent expert system of inferences from assertions of partial knowledge. One session of our workshop was devoted to understanding the formulation and computational structure of this theorem, as explained in the articles1 by Lad, Dickey, and Rahman (1990, 1992). In a word, the fundamental theorem of prevision identifies numerically the coherent implications of any partial prevision assertions (including interval probabilities) for any other cohering prevision or conditional prevision whatsoever. The present paper was discussed at a second session, and presumes the reader’s familiarity with these expositions. For the purpose of self-containment here, a brief summary of the definitions, notation, and theorems that lead to the fundamental theorem of prevision in a finite, discrete context, and a concise statement of the theorem in both its parts are appended to the end of this article. They are excerpted from the forthcoming text by Lad (1994). Included in the excerpt are definitions and a basic theorem pertaining to the judgment to regard a sequence of quantities exchangeably, which are also relevant to developments in the present article.