Additive Utility Without Restricted Solvability on Every Component
Résumé
It is shown that restricted solvability need not be required to hold w.r.t. every component for deriving the existence of additive utilities: additive representations can be shown to exist even when restricted solvability holds w.r.t. only two components. In such cases, the uniqueness property of these representations departs from the classical theory in that it is between ordinal and cardinal.