Abstract

A choice function is rational if it describes the maximization of a preference relation. There are a variety of conditions that a preference relation can satisfy. We focus on orders, a complete and transitive relation. While alpha and beta characterize choice functions normalized by an order, they do not characterize all choice functions that describe the maximization of an order. We show that lambda and mu characterize choice functions that are representable by an order. The difference between a normal and a representable choice function is that the former assumes that if two alternatives are in the image of a choice set, then the two alternatives are indifferent. Representability does not make this assumption. A distinction between the ordering properties of a preference relation and the uniformity of a family of preference relations is drawn. A family of preference relations $\{$R$\sb{\rm s}\}$ is uniform if and only if R$\sb{\rm s}$ restricted to S$\sp\prime$ equals R$\sb{\rm s}\sp\prime$. We argue that the failures of transitivity of a preference relation are better expressed as failures of uniformity, and suggest that not all failures of uniformity are failures of rationality