  Axelrod (1997) showed how local convergence in cultural influence can
preserve cultural diversity. We argue that central implications of Axelrod's
model may change profoundly, if his model is integrated with the assumption of
social influence as assumed by an earlier generation of modelers. Axelrod and
all follow up studies employed instead the assumption that influence is
interpersonal (dyadic). We show how the combination of social influence with
homophily allows solving two important problems. Our integration of social
influence yields monoculture in small societies and diversity increasing in
population size, consistently with empirical evidence but contrary to earlier
models. The second problem was identified by Klemm et al.(2003a,b), an
extremely narrow window of noise levels in which diversity with local
convergence can be obtained at all. Our model with social influence generates
stable diversity with local convergence across a much broader interval of noise
levels than models based on interpersonal influence.
