RYTINA, STEVEN LAWRENCE; PHD

                         THE UNIVERSITY OF MICHIGAN, 1980

                         SOCIOLOGY, THEORY AND METHODS (0344)
 

                         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.

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