Rationalizability of Choice Functions: Domain Conditions

Abstract

In the literature related to choice theory an important problem which has been dealt at length is the rationalizability of choice function. In the approach of revealed preference theory the question generally posed is whether it is possible to explain the demand function from the choice behaviour of the individual itself without invoking any preference relation. It is asked in this context whether it is possible to construct a preference relation observing choices under different environments, such that the chosen elements of a set are the same elements as the set of best elements of the set according to that preference relation. In the literature of choice theory this problem is known as the rationalizability of choice function. This problem investigates whether there is any basis of choices made under different environments. It has been established that a choice function is rationalizable if and only if it satisfies some choice consistency conditions namely, Houthakker’s axiom of revealed preference, Hansson’s axiom of revealed preference etc. Most of these choice consistency conditions which characterize a rationalizable choice function put constrains on the choice function itself and thereby on the choice behaviour of the individual. In this paper we propose a new set of conditions which unlike restricting the choice behaviour of an individual puts constraints on the domain of the choice functions. This paper shows that every choice function defined over a domain which satisfies those conditions will be rationalizable. Thus in the literature we find characterization of partitions between rationalizable and non rationalizable choice functions, on the contrary, this paper provides full characterization of partition of domains where on one side there are domains over which every choice function is rationalizable, and on the otherside there are domains over which not all choice functions are rationalizable..