Similarity Measures on Preference Structures, Part II: Utility Functions

In previous work [8] we presented a casebased approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic distance as a measure of similarity on user preferences, and provided an algorithm to compute the distance between two partially specified value functions. This is for the case of decision making under certainty. In this paper we address the more challenging issue of computing the probabilistic distance in the case of decision making under uncertainty. We present algorithms to compute the probabilistic distance between two completely or partially specified utility functions. We demonstrate the use of this algorithm with a medical data set of partially specified patient preferences, where none of the other existing distance measures appear definable. Using this data set, we also demonstrate that the case-based approach to preference elicitation is applicable in domains with uncertainty.