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 behaviour for a population to organise itself into a relatively small number of societies? In a companion paper we characterised how large å 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.