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Threshold Behavior of Democratic Opinion Dynamics

Abstract

Consider a community where initially, each individual is positive or negative regarding a reform proposal. In each round, individuals gather randomly in fixed rooms of different sizes, and all individuals in a room agree on the majority opinion in the room (with ties broken in favor of the negative opinion). The Galam model—introduced in statistical physics, specifically sociophysics—approximates this basic random process. We approach the model from a more mathematical perspective and study the threshold behavior and the consensus time of the model.

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Fig. 1

Notes

  1. 1.

    We say an event occurs asymptotically almost surely (a.a.s.) if its probability is at least \(1-o\left( 1\right) \) as a function of n.

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Acknowledgements

We wish to thank Serge Galam for referring to some prior works.

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Correspondence to Ahad N. Zehmakan.

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Communicated by Irene Giardina.

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Gärtner, B., Zehmakan, A.N. Threshold Behavior of Democratic Opinion Dynamics. J Stat Phys 178, 1442–1466 (2020). https://doi.org/10.1007/s10955-020-02515-1

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Keywords

  • Galam model
  • Opinion dynamics
  • Threshold behavior
  • Consensus time
  • Majority rule