This paper grew out of a reading of an interesting exposition by Danilov and Sotskov [1997], where general one to one correspondences are established between binary relations and choice correspondences. Out purpose in this paper is to establish similar and more specific bisections in choice situations that arise in social choice theory. The kind of domain we consider here, has not been considered by Danilov and Sotskov [1997]. We consider social choice problems of the type discussed in the literature on axiomatic bargaining. Instead of choice functions, we consider choice correspondences i.e. multivalued solutions. Expositions of the main results in axiomatic bargaining can be found in Thomson [1994] and an economic interpretation of the problems can be found in Lahiri [1996]. Earlier forays into rational choice theory on such domains are those of Peters and Wakker [1991], and Lahiri [1998].