Prospect theory and stochastic multicriteria acceptability analysis (SMAA)

We consider problems where multiple decision makers (DMs) want to choose their most preferred alternative from a finite set based on multiple criteria. Several approaches to support DMs in such problems have been suggested. Prospect theory has appealed to researchers through its descriptive power, but rare attempts have been made to apply it to support multicriteria decision making. The basic idea of prospect theory is that alternatives are evaluated by a difference function in terms of gains and losses with respect to a reference point. The function is suggested to be concave for gains and convex for losses and steeper for losses than for gains. Stochastic multicriteria acceptability analysis (SMAA) is a family of multicriteria decision support methods that allows representing inaccurate, uncertain, or partly missing information about criteria measurements and preferences through probability distributions. SMAA methods are based on exploring the weight and criteria measurement spaces in order to describe weights that would result in a certain rank for an alternative. This paper introduces the SMAA-P method that combines the piecewise linear difference functions of prospect theory with SMAA. SMAA-P computes indices that measure how widely acceptable different alternatives are with assumed behavior. SMAA-P can be used in decision problems, where the DMs’ preferences (weights, reference points and coefficients of loss aversion) are difficult to assess accurately. SMAA-P can also be used to measure how robust a decision problem is with respect to preference information. We demonstrate the method by reanalyzing a past real-life example.