ABSTRACT
Social processes, such as fads, social movements, pandemics and even crime are driven by peer-effects and can be understood as social cascades in which a small initial number of actors are joined by an ever-growing number of other members of society.
This chapter studies these pervasive social dynamics and introduces the reader to the threshold model, in which individuals take actions or share a belief based on the number of other individuals they observe doing likewise. At its core and in contrast to most of the other approaches studied in this book, dynamics are critically dependent on inherent differences between individuals. Another characteristic of this approach is even more striking. Populations with very minor preferential or structural differences can illustrate fundamentally different social dynamics. The chapter examines the impact of absolute and relative group sizes, as well as tolerances and preferences, on social dynamics, and shows how situations evolve in which observable public opinion or action is not representative of the collective beliefs or actions of members of society.
Among the concepts discussed are: positive, normative, and preferential imitation, as well as iterated maps, and the stability of discrete dynamical systems.
