Similarity Measures on Preference Structures, Part II: Utility Functions
This work addresses preference elicitation in uncertain domains, such as medical decision-making, but is incremental as it extends prior methods from certainty to uncertainty.
The paper tackles the problem of computing similarity between user preferences under uncertainty by providing an algorithm for the probabilistic distance between partially specified utility functions, demonstrating its applicability on a medical dataset where other measures fail.
In previous work cite{Ha98: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 under{em 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.