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Binary consensus via exponential smoothing

: Montes de Oca, M.A.M.; Ferrante, E.; Scheidler, A.; Rossi, L.F.


Glass, K.:
Complex Sciences. Second International Conference, COMPLEX 2012 : Santa Fe, NM, USA, December 5-7, 2012, Revised Selected Papers
Cham: Springer International Publishing, 2013 (Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 126)
ISBN: 978-3-319-03472-0 (Print)
ISBN: 978-3-319-03473-7 (Online)
International Conference on Complex Sciences (COMPLEX) <2, 2012, Santa Fe/NM>
Conference Paper
Fraunhofer IWES ()

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.