Similarity Measures on Preference Structures, Part II: Utility Functions
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In previous work citeHa98:Towards we presented a case-based 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 em value functions. This is for the case of decision making under em certainty. In this paper we address the more challenging issue of computing the probabilistic distance in the case of decision making underem uncertainty. We provide an algorithm to compute the probabilistic distance between two partially specified em 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 distancemeasures appear definable. Using this data set, we also demonstrate that the case-based approach to preference elicitation isapplicable in domains with uncertainty. Finally, we provide a comprehensive analytical comparison of the probabilistic distance with some existing distance measures on preferences.
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