On The Distance Between Cp-Nets

Preferences play a key role in decision making by both single individuals and/or groups. In a multi-agent context, it is also important to know how to aggregate preferences to reach a collective decision. Moreover, being able to measure the distance between the preference of two individuals is important to identify the amount of disagreement and possibly reach consensus. In this paper we define a notion of distance between CP-nets, a formalism that can compactly encode conditional qualitative preferences. We consider the Kendall-tau distance between the partial orders induced by CP-nets, and we define two tractable approximations of that distance, which can be computed in time polynomial in the number of features of the CP-nets. We then perform experiments to demonstrate the quality of these approximations compared to the Kendall-tau distance. We also relate our two notions of distance to the distance rationalizability of sequential plurality voting for CP-nets.