Binary Consensus via Exponential Smoothing

  • Marco A. Montes de Oca
  • Eliseo Ferrante
  • Alexander Scheidler
  • Louis F. Rossi
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 126)


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.


Consensus Collective Decision-Making Self-Organization Swarm Intelligence 


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© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2013

Authors and Affiliations

  • Marco A. Montes de Oca
    • 1
  • Eliseo Ferrante
    • 2
    • 3
  • Alexander Scheidler
    • 4
  • Louis F. Rossi
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DelawareUSA
  2. 2.IRIDIA, CoDEUniversité Libre de BruxellesBelgium
  3. 3.Socioecology and Social Evolution LabKatholieke Universiteit LeuvenBelgium
  4. 4.Fraunhofer IWESGermany

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