Su una classe di relazioni di preferenza equivalenti ad una relazione regolare

In the context of revealed preference theory, two irreflexive (or "strong preference") relations are said to be ("motivationally") "equivalent" if and only if they generate, by means of the usual process of constrained maximization, the same demand correspondence. The traditional economic theory is particularly interested in the case in which among the strong preference relations generating a demand correspondence there is a "regular" relation, i.e. a transitive relation whose non-comparability relation is transitive too. However, the relations which are equivalent to a regular relation are not necessarily regular. Therefore, the following problem naturally arises: what properties a strong preference relation must possess in order that among its equivalent relations there is a regular relation? To this end, it is sufficient to suppose that: a) the separating hyperplane between any consumption vector and the set of its preferred elements is unique; b) every non-empty and finite set of consumption vectors is not included in the convex hull of the union of the preferred elements to the points of the set.