  One of the fundamental principles driving diversity or homogeneity in domains
such as cultural differentiation, political affiliation, and product adoption
is the tension between two forces: influence (the tendency of people to become
similar to others they interact with) and selection (the tendency to be
affected most by the behavior of others who are already similar). Influence
tends to promote homogeneity within a society, while selection frequently
causes fragmentation. When both forces act simultaneously, it becomes an
interesting question to analyze which societal outcomes should be expected.
  To study this issue more formally, we analyze a natural stylized model built
upon active lines of work in political opinion formation, cultural diversity,
and language evolution. We assume that the population is partitioned into
"types" according to some traits (such as language spoken or political
affiliation). While all types of people interact with one another, only people
with sufficiently similar types can possibly influence one another. The
"similarity" is captured by a graph on types in which individuals of the same
or adjacent types can influence one another. We achieve an essentially complete
characterization of (stable) equilibrium outcomes and prove convergence from
all starting states. We also consider generalizations of this model.
