Social organizations and matching theory

We generalize the Gale-Shapley matching theory to the formation of social units consisting of more than two individuals and each individual having more than one role.We show how social preferences and social structure could conflict with freedom. In the absence of such a conflict, we define stability and show that this could conflict with social preferences and social structure. Next, we define Rawlsian justice in case of stability and show how social preferences and social structure can conflict with justice. Thus, it is the social preferences and social-structure which decide whether our concepts of freedom, stability, and justice are achievable or not.