Chernoff and a new congruence axiom implies full rationality

Abstract

Rationality in choice theory has been an abiding concern of decision theorists. A rationality postulate of considerable significance in the literature is the weak congruence axiom of Richter (1971) and Sen (1971). It is well known that in discrete choice contexts of the classical type (i.e. all nonempty finite subsets of a given set comprise the set of choice problems), this axiom is equivalent to full rationality. The question is: whether a (considerable?) weakening of the weak congruence axiom would suffice to imply full rationality? This is the question we take up in this paper. We propose a weaker new congruence axiom which along with the (mother of all axioms? Chernoff Axiom implies full rationality. The two axioms are independent. We also study interesting properties of these axioms and their interconnections through examples. Rationality in choice theory has been an abiding concern of decision theorists. A rationality postulate of considerable significance in the literature is the weak congruence axiom of Richter (1971) and Sen (1971). It is well known that in discrete choice contexts of the classical type (i.e. all nonempty finite subsets of a given set comprise the set of choice problems), this axiom is equivalent to full rationality. The question is: whether a (considerable?) weakening of the weak congruence axiom would suffice to imply full rationality? This is the question we take up in this paper. We propose a weaker new congruence axiom which along with the (mother of all axioms? Chernoff Axiom implies full rationality. The two axioms are independent. We also study interesting properties of these axioms and their interconnections through examples.