Sid Redner (Physics Department, Boston University and SFI External Professor)
Abstract: In many models of social dynamics, some attribute is transferred by a single interaction between agents that causes an agent to change its state. What happens, however, if an agent requires multiple signals from its neighbors before changing state? The result is quite rich. We first present a simple fad propagation model in which an agent adopts the fad only after receiving K inputs to adopt from other agents. For a population size N, the time until the fad is adopted scales as ln N for k=1, and N^{(K-1)/K} for K>1. For the voter model with K inputs needed to change state, a two-time scale approach to consensus is found. There is a manifold of initial conditions that leads the population to almost immediately reach an "apathetic" state before consensus is reached in a time that scales as ln N.