Utility Copula Functions Matching All Boundary Assessments

Abstract

The construction of a multiattribute utility function is an important step in decision analysis and can be a challenging task unless some decomposition of the utility function is performed. When every attribute is utility independent of its complement, the utility elicitation task is significantly simplified because the functional form of the utility function requires only one conditional utility function for each attribute, and some normalizing constants. When utility independence conditions do not hold, the conditional utility function of an attribute may vary across the domain of the complement attributes, and therefore a single conditional utility assessment for each attribute may not be sufficient to capture the decision maker's preferences. This paper proposes a method to construct utility functions that have the flexibility to match the variations in the conditional utility function, across the domain of the attributes, using univariate utility assessments at the boundary values. The approach incorporates the boundary assessments into a new function, which we call the double-sided utility copula. This formulation provides a wealth of new functional forms that the analyst may use to incorporate utility dependence in multiattribute decision problems. The utility copula function also allows for the flexibility to incorporate a wide range of trade-off assessments among the attributes, while keeping the utility assessments at the boundary values fixed. It is also useful in determining the order of approximation provided by using certain independence assumptions in a multiattribute decision problem when the attributes are utility dependent.