An Extension Theorem for Rational Choice Functions

A choice function is strictly rational whenever it can be rationalized by a preference relation in a manner such that alternatives in a choice set are strictly preferred to alternatives in the corresponding rejection set. We demonstrate an Extension Theorem which asserts that a preference relation strictly rationalizes the choice function if and only if the choice function satisfies the Weak Axiom of Revealed Preference and the preference relation is an extension of the revealed weak preference relation. Then we consider various applications to rational choice theory.