In many interactive decision making scenarios there is often no solution that satisfies all of the user's preferences. The decision process can be helped by providing explanations. Relaxations show sets of consistent preferences and, thus, indicate which preferences can be enforced, while exclusion sets show which preferences can be relaxed to obtain a solution. We propose a new approach to explanation based on the notion of a representative set of explanations. The size of the set of explanations we compute is exponentially more compact than that found using common approaches from the literature based on finding all minimal conflicts. Copyright © 2007, Association for the Advancement of Artificial Intelligence ( All rights reserved.