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Analytic treatment of consensus achievement in the single-type zealotry voter model

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  • Fudolig, Mikaela Irene D.
  • Esguerra, Jose Perico H.

Abstract

We introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement. Using first-step analysis for Markov chains to obtain an exact solution, we find that the mean consensus time scales with the population size N. Increasing the number of zealots, Z, will decrease the consensus time in a power law fashion for large Z. The mean magnetization was also analytically obtained and was found to contain an exponential dependence on Z. The dynamics for the complete graph are qualitatively similar to those obtained in another study for the Barabasi–Albert network. In general, the existence of zealots serves to hasten consensus, except in the case where only a few zealots oppose the vast majority.

Suggested Citation

  • Fudolig, Mikaela Irene D. & Esguerra, Jose Perico H., 2014. "Analytic treatment of consensus achievement in the single-type zealotry voter model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 626-634.
    • Handle: RePEc:eee:phsmap:v:413:y:2014:i:c:p:626-634
    DOI: 10.1016/j.physa.2014.07.033
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    References listed on IDEAS

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    1. Kashisaz, Hadi & Hosseini, S. Samira & Darooneh, Amir H., 2014. "The effect of zealots on the rate of consensus achievement in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 49-57.
    2. Galam, Serge & Jacobs, Frans, 2007. "The role of inflexible minorities in the breaking of democratic opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 366-376.
    3. Verma, Gunjan & Swami, Ananthram & Chan, Kevin, 2014. "The impact of competing zealots on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 310-331.
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    Cited by:

    1. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.

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