Threshold Models of Diversity: Chinese Restaurants, Residential Segregation and the Spiral of Silence

Abstract:

In many binary decisions, a person 's choice depends in part on the composition of the group that has already made one or the other choice. In deciding whether to live in a neighborhood, a person may consider the ethnic composition of the neighborhood. In deciding whether to speak out on a public issue, a person may consider the proportion of previously expressed opinions that are the same as his. Substantial literatures have grown up around these two examples, which go under the rubrics of residential tipping and pluralistic ignorance. We develop a mathematical model that applies to all such binary situations and illustrate it especially by the examples of residential segregation and public opinion. The model builds on and generalizes previous work on these subjects, and it is related to but distinct from the authors' earlier work on threshold models of collective behavior. We conclude with a report on preliminary attempts at empirical measurement.