O Axioma da Transitividade é Supérfluo?

Abstract

This paper is concerned with a discussion about the necessity of a transitivity axiom in choice theory. The best known attempts to dismiss the transitivity property employ the convexity condition. In this article we show that the convexity condition implies transitivity in all linear directions. We provide then a simple proof of the existence of a demand correspondence in a two-dimensional commodity space without imposing an explicit transitivity condition. A brief discussion on the meaning of the transitivity property that is implicit in the convexity condition concludes the paper.