A note on the asymmetric part of an outranking relation

This note discusses the properties of the asymmetric part of an outranking relation a la ELECTRE. Such relations have been used in the pseudodisjunctive version of ELECTRE TRI-B. We show that they have properties that are somewhat di erent from the ones of outranking relations. Indeed, contrary to outranking relations, they allow to have at the same time veto and bonus e ects. We suggest that this explains the di culty in analyzing the properties of the pseudo-disjunctive version of ELECTRE TRI-B and the complexity of the elicitation methods of its parameters. We give conditions that characterize such relations.