Social organizations and matching theory
The paper generalizes the Gale-Shapley matching theory [see \textit{D. Gale} and \textit{L. S. Shapley}, Amer. Math. Monthly 69, 9-15 (1962; Zbl 0109.244)] to the formation of social units consisting of more than two individuals and each individual having more than one role. The authors define ``freedom'' through matching mechanism and show how it could conflict with social preferences (SP) and social structure (SS). In case that such a conflict doesn't exist, stability is defined and in turn this is shown to be in conflict with SP and SS. This conflict may be resolved due to restricting ``freedom'' with the aid of ``stabilizing'' regulations. Another conflict is shown between SP/SS and ``justice'' in case of stability. Thus, in this model, SP/SS are shown to decide whether the concepts ``freedom'', ``stability'' and ``justice'' are achievable or not. The rather complicated terminology of the paper is based on set- theoretical topics and graphs using some algebraic considerations on preferences.
scientific article; zbMATH DE number 4043673
scientific article