Additive Utility with Intransitive Indifference and without Independence: A Homogeneous Case

Abstract

In the homogeneous case of one type of goods or objects, we prove the existence of an additive utility function without assuming transitivity of indifference and independence. The representation reveals a positive factor smaller than 1 that infuences rational choice beyond the utility function and explains departures from these standard axioms of utility theory (factor equals to 1).