A folk meta-theorem in the foundations of utility theory

Abstract

We formalize a folk meta-theorem, which we call the Coduality Principle, that unifies the weak and strict preference approaches to utility theory. The Coduality Principle asserts that any well-formed formula involving weak preference is equivalent to a codual formula involving strict preference that is obtained by replacing every occurence of a weak preference relation in the original formula with an equivalent codual relation. We also provide some of the history, theory, and applications of the Coduality Principle to decision theory.