Rationalizability And Domain Condition: A Note

In the literature related to choice theory an important problem which has been dealt at length is the rationalizability of choice function. In the context of set-valued choice function, this problem poses the following question: is it 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. This problem investigates whether there is any basis of choices made under different environments. The literature resorts to this problem by introducing a number of choice consistency conditions which in effect have been proved to be necessary and sufficient for ordering rationalization. Most of these choice consistency conditions are of the nature that they impose restrictions on the choice function and thereby on the choice behaviour of an individual. This paper proposes a new set of conditions which unlike restricting the choice behaviour of an individual puts constraints on the domains of choice func-tions. The paper also discusses the merit of considering domain conditions as opposed to consistency conditions and mentions the results obtained therein.