A Generalized Sampling Approach for Multilinear Utility Functions Given Partial Preference Information

The assessment and characterization of multilinear utility functions (MLUFs) may require the elicitation of many attribute weights. In this case, the decision maker may find it difficult to provide precise assessments and may instead be more comfortable providing a range in which the scaling parameters fall or specifying that some parameters are larger than others. The question then becomes how the analyst should formulate a recommendation given this partial preference information. In this paper, we present a generalized Monte Carlo simulation procedure to test the sensitivity of MLUFs to changes in the scaling parameters. Specifically, we admit any preference information that can be expressed as a linear constraint. We then sample from the set of all possible MLUFs matching these constraints. We consider the additive MLUF, the multiplicative MLUF, the utility-independent MLUF, and the generalized utility-independent MLUF. In so doing, we also demonstrate how analysts can test the sensitivity of their analysis to the structure of the MLUF itself. We illustrate the flexibility of our method within the context of a coal-fired power plant siting decision used by previous authors.