Abstract
People's behavior is informed and influenced by other people's choices. In many online technologies, for instance, aggregate information about the choices of other individuals is encoded in the form of rankings. Such rankings, in turn, have a direct impact on people's future choices. What are the long-term dynamics of these rankings, and do the dynamics depend on specific assumptions about people's behavior? In this paper, we propose a general framework for modeling the dynamics in settings where information about peoples' past choices is recorded as a ranking and influences future choices. We find a general condition for convergence, show that it is satisfied by many important models in economics and beyond, and characterize the possible limits in terms of the choice probabilities.