Similarity of personal preferences: Theoretical foundations and empirical analysis

We study the problem of defining similarity measures on preferences from a decision-theoretic point of view. We propose a similarity measure, called probabilistic distance, that originates from the Kendall's tau function, a well-known concept in the statistical literature. We compare this measure to other existing similarity measures on preferences. The key advantage of this measure is its extensibility to accommodate partial preferences and uncertainty. We develop efficient methods to compute this measure, exactly or approximately, under all circumstances. These methods make use of recent advances in the area of Markov chain Monte Carlo simulation. We discuss two applications of the probabilistic distance: in the construction of the Decision-Theoretic Video Advisor (diva), and in robustness analysis of a theory refinement technique for preference elicitation.