Complete characterization of domains of choice functions for rationalizability

In the literature related to choice theory an important problem dealt at length is the rationalizability of choice function of an individual. In the literature a number of choice consistency conditions have been postulated, which guarantee best element and maximal element rationalizability of choice functions. In this paper a set of necessary and sufficient conditions have been derived for the domain to be such that every possible choice function defined over the domain has a best element (maximal element) rationalization. Thus the paper provides complete characterization of partition of domains separately for best and maximal element rationalizable choice functions.