Note—A Comment on Blau's Dilemma in “Stochastic Programming” and Bayesian Decision Analysis

Abstract

Using what he calls a “Basic Chance Constrained Programming Model,” BCCM, R. A. Blau proceeds in Blau [Blau, R. A. 1974. Stochastic programming and decision analysis: an apparent dilemma. Management Sci. 21 (3, November) 271–276.] to derive some results which he believes lead to a dilemma in which EPVI, the Expected Value of Perfect Information, is less than EVSI, the Expected Value of Sample Information. This is one part of Blau's dilemma. In addition, EPVI and EVSI are both negative. This is the other part of Blau's dilemma, from which he goes on to a variety of philosophic and other objections that he believes relate to contrasts between Bayesian decision theory and other, more classic, approaches in statistics. The latter are, in turn, related to chance constrained programming, and so on, but in ways that are only adumbrated rather than developed in detail by Blau.

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