On the non-equivalence of weak and strict preference

Abstract

It is often claimed that the relations of weak preference and strict preference are symmetrical to each other in the sense that weak preference is complete and transitive if and only if strict preference is asymmetric and negatively transitive. The equivalence proof relies on a definitional connection between them, however, that already implies completeness of weak preference. Weakening the connection in order to avoid this leads to a breakdown of the symmetry which gives reason to accept weak preference as the more fundamental relation.