The number of organizations in heterogeneous societies

I consider a society with heterogeneous individuals who can form organizations for the production of a differentiated service. An arrangement of organizations is said to be split up stable when there is no majority to split any of the organizations. Unlike other equilibrium concepts in the literature, the largest number of organizations that is split up stable corresponds to the socially optimal number of organizations, with a possibility of over provision of one organization. The analysis is extended to a case with endogeneous membership, where it is shown that the results remain the same.