The shape of the utility or value function in stochastic multicriteria acceptability analysis

Abstract

Stochastic multicriteria acceptability analysis (SMAA) is a decision support method that allows representing uncertain, imprecise, and partially missing criteria measurements and preference information as probability distributions. In this paper, we test how the assumed shape of the utility or value function affects the results of SMAA in two different problem settings: identifying the most preferred alternative and ranking all the alternatives. A linear value function has been most frequently applied, because more precise shape information can be difficult to obtain in real-life applications. In this paper, we analyse one past real-life problem and a large number of randomly generated test problems of different size using additive functions of different shape. The shape varies from linear to increasingly concave and convex exponential utility or value functions corresponding to different attitudes on marginal value or risk. The results indicate that in most cases slight non-linearity does not significantly affect the results. The proposed method can be used for evaluating how robust a particular real-life decision problem is with respect to the shape of the function. Based on this information, it is possible to determine how accurately the DMs' preferences need to be assessed in a particular problem, and if it is possible to assume a simple linear shape.