In this paper we attempt to arrive at axiomatic characterizations of choice functions which are subrational and where chosen elements are a subset of the solution set obtained by maximizing a binary relation. We also try to provide axiomatic characterizations of choice functions where choice sets contain atleast one solution obtained by maximizing a binary relation. We call such choice functions quasirational. A particular type of quasirational choice functions are what we call consistent choice functions. We provide an axiomatization of such solutions in this paper as well