The constructive inequivalence of various notions of preference ordering

Abstract

Three classically equivalent notions - classical preference relation, weak preference relation, and preference relation - are discussed within the framework of recursive constructive mathematics. It is shown that the implications preference relation ⇒ weak preference relation ⇒ classical preference relation are the best possible in that framework; but that under certain conditions, including two (openness and local nonsatiation) that arise naturally in economic theory, a weak preference relation is a preference relation.