Differentiation Reconsidered: Social Networks and Macro-Theory.

Abstract

Mathematical models of the flows of contact within and between social categories are developed. The model for two categories reveals that the smaller category is more dense, more outbred, and more sensitive to changes in parameters. N-category models are shown to be a weighted average of two-category models. Multi-dimensional models for the special case of uncorrelated dimensions are developed. Both models imply the surprising result that increases in the number of categories and number of dimensions, interpreted as increases in social differentiation, lead to increases in sociometric density, interpreted as social cohesion, that far outstrip the more expectable increases in inter-category contact. A model of logically perfect cross-cutting pluralism, where every status is uncorrelated with every other status, reveals dense networks, no decline in category boundaries, and latent conflict groups arrayed on a hierarchical dimension. The models form the basis of a critique of Wirth's theory of urbanism. The pattern of resource distribution to which Dahl attributed pluralist politics is shown to follow from the structural changes from which Mills derived a power elite. A critique of conceptions of urban political integration considers networks as the link between structural categories and collective action. Finally, the macro network models are compared with older traditions in network analysis.