Patchwork Constructions of Multiattribute Utility Functions

Abstract

The construction of a representative multiattribute utility function is important in decision analysis. Existing methods focus mainly on constructions of utility functions on the whole domain of attributes. In some cases, decision makers may provide partial information on their local utility assessments. Therefore, it is a challenging and interesting task to construct utility functions that are compatible with local assessments provided by decision makers. This paper proposes the patchwork construction to accomplish this task. We first define a special local preference structure, the local utility independence and then discuss the patchwork construction that unifies local utility independence on different local domains. The utility function elicited by the patchwork approach under the local utility independence condition is named as the local-utility-independent utility function. Three types of local-utility-independent utility functions on three typical partitions are proposed. These local-utility-independent utility functions have concise and tractable functional forms and indicate intuitive preference structures while matching prior known local utility assessments. Furthermore, the preference structures implied by these three types of local-utility-independent utility functions have a close relationship with the n-switch independence. Sufficient and necessary conditions guaranteeing these local-utility-independent utility functions to indicate n-switch independence are provided, respectively. All three types of local-utility-independent utility functions also have an important application in the approximations of arbitrary utility functions when only some local assessments are provided. As approximations, they are robust and have high accuracy.