Mathematical sociology uses highly formalized models to understand social processes and social structures. Agent-based models, for example, understand social life as a function of interactions among adaptive agents who influence one another in response to the influence they receive. These models allow sociologists to understand how simple and predictable local interactions between agents can generate familiar global patterns of social structure. They can also be used to perform virtual experiments that test macrosociological theories by manipulating structural factors like network topology, social stratification, or spatial mobility.
Mathematical sociologists at Cornell have studied the diffusion of business fads; the emergence of unpopular norms; the conditions under which agents participate in collective action; cross-national differences in trust; and how powerful agents use their position in an exchange network to advance their interests.