Binary Consensus via Exponential Smoothing

Abstract

In this paper, we reinterpret the most basic exponential smoothing equation, S ^t + 1 = (1 − α)S ^t + αX ^t, as a model of social influence. This equation is typically used to estimate the value of a series at time t + 1, denoted by S ^t + 1, as a convex combination of the current estimate S ^t and the actual observation of the time series X ^t. In our work, we interpret the variable S ^t as an agent’s tendency to adopt the observed behavior or opinion of another agent, which is represented by a binary variable X ^t. 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.