Interpret a set of players all playing the same pure strategy and all with similar attributes as a society. Is it consistent with self interested behavior for a population to organize itself into a relatively small number of societies? In a companion paper we characterized how large ε must be, in terms of parameters describing individual games, for an equilibrium to exhibit conformity in pure strategies. In this paper we provide a wide class of games where such conformity is boundedly rational, that is, where can be chosen to be small.