Preferences for multi - attributed alternatives : Traces , Dominance , and Numerical Representations 1

1 Part of this work was accomplished while Denis Bouyssou was visiting the Service de Mathématiques de la Gestion at the Université Libre de Bruxelles (Brus-sels, Belgium). He gratefully acknowledges the warm hospitality of the Service de Mathématique de la Gestion as well as the support of the Belgian Fonds National de la Recherche Scientifique and the Brussels-Capital Region through a " Research in Brussels " action grant.The other part of this work was accomplished while Marc Pirlot was visiting LIP6–Université Pierre et Marie Curie and LAMSADE– Université Paris Dauphine (Paris, France) thanks to visiting positions in these two institutions and a grant from the Fonds National de la Recherche Scientifique. He gratefully acknowledges this support.