Two theoretical models are developed to examine the individual incentives and perceptions of difference between people that can lead, collectively, to the segregation of various sub-populations. The models also clarify the extent to which inferences can be drawn from the phenomenon of collective segregation about the preferences of individuals, the strengths of those preferences, and the facilities for exercising them. The first of these two conceptual models is a simulation model that distributes individuals within an area in accordance with their preferences about the composition of the neighborhood. The variables are the ratio of the two races in the population, the demands for neighbors like oneself, and the size of the neighborhood within which an individual’s preferences operate. The second model, which is analytical, examines the questions: What distribution of color tolerances among the population may be compatible with dynamically stable mixtures? What effect will the initial conditions and the dynamics of movement have on the outcome? What kinds of numerical constraints might alter the results? Use of the formal model to examine the phenomenon of neighborhood tipping does not reveal any important discontinuity necessarily occurring at the commonly accepted tolerance value of 20 percent black.