Differential Utility: Accounting for Correlation in Performance Among Design Alternatives

Abstract

Recognizing expected utility as a valid design criterion, there are cases where uncertainty is such that this criterion fails to distinguish clearly between design alternatives. These cases may be characterized by broad and significantly overlapping utility probability distributions. Not uncommonly in such cases, the utility distributions of the alternatives may be highly correlated as the result of some uncertain variables being shared by the alternatives, because modeling assumptions may be the same across alternatives, or because difference information may be obtained by means of an independent source. Because expected utility is evaluated for alternatives independently, maximization of expected utility typically fails to take these correlations into account, thus failing to make use of all available design information. Correlation in expected utility across design alternatives can be taken into account only by computing the expected utility difference, namely the “differential expected utility,” between pairs of design alternatives. However, performing this calculation can present significant difficulties of which excessive computing times may be key. This paper outlines the mathematics of differential utility and presents an example case, showing how a few simplifying assumptions enabled the computations to be completed with approximately 24 hours of desktop computing time. The use of differential utility in design decision making can, in some cases, provide significant additional clarity, assuring better design choices.