Binary consensus via exponential smoothing

Abstract

In this paper, we reinterpret the most basic exponential smoothing equation, St+1 = (1 − α)St + αXt, as a model of social influence. This equation is typically used to estimate the value of a series at time t + 1, denoted by St+1, as a convex combination of the current estimate St and the actual observation of the time series Xt. In our work, we interpret the variable St as an agent’s tendency to adopt the observed behavior or opinion of another agent, which is represented by a binary variable Xt. We study the dynamics of the resulting system when the agents’ recently adopted behaviors or opinions do not change for a period of time of stochastic duration, called latency. Latency allows us to model real-life situations such as product adoption, or action execution. When different latencies are associated with the two different behaviors or opinions, a bias is produced. This bias makes all the agents in a population adopt one specific behavior or opinion. We discuss the relevance of this phenomenon in the swarm intelligence field.