What Kind of Preference Maximization Does the Weak Axiom of Revealed Non-inferiority Characterize?

A multi-valued choice is weak justified if no chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is <i>some</i> chosen alternative which dominates it. This definition allows us to build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a weak notion of rationality. Our notion of rationaity is weaker than that characterized by the weak axiom of revealed preference.