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The noisy voter model under the influence of contrarians

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  • Khalil, Nagi
  • Toral, Raúl

Abstract

The influence of contrarians on the noisy voter model is studied at the mean-field level. The noisy voter model is a variant of the voter model where agents can adopt two opinions, optimistic or pessimistic, and can change them by means of an imitation (herding) and an intrinsic (noise) mechanisms. An ensemble of noisy voters undergoes a finite-size phase transition, upon increasing the relative importance of the noise to the herding, form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states. By the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents (anti-herding). We first consider the case of only contrarians and show that the only possible steady state is the unimodal one. More generally, when voters and contrarians are present, we show that the bimodal-unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four, and their characteristic rates are small enough. For the number of contrarians bigger or equal to four, the voters and the contrarians can be seen only in the unimodal phase. Moreover, if the number of voters and contrarians, as well as the noise and herding rates, are of the same order, then the probability functions of the steady state are very well approximated by the Gaussian distribution.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:81-92
    DOI: 10.1016/j.physa.2018.09.178
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    1. 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.
    2. A. Corcos & J-P Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2002. "Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaos," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 264-281.
    3. Galam, Serge, 2000. "Real space renormalization group and totalitarian paradox of majority rule voting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 66-76.
    4. Galam, Serge, 2004. "Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 453-460.
    5. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2015. "Markets, herding and response to external information," Papers 1506.03708, arXiv.org, revised Jun 2015.
    6. Adrián Carro & Raúl Toral & Maxi San Miguel, 2015. "Markets, Herding and Response to External Information," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-28, July.
    7. 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.
    8. M. S. de la Lama & I. G. Szendro & J. R. Iglesias & H. S. Wio, 2006. "Van Kampen's expansion approach in an opinion formation model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(3), pages 435-442, June.
    9. 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.
    10. Adri'an Carro & Ra'ul Toral & Maxi San Miguel, 2016. "The noisy voter model on complex networks," Papers 1602.06935, arXiv.org, revised Apr 2016.
    11. Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
    12. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 137-156.
    13. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    14. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    15. Galam, Serge, 2011. "Collective beliefs versus individual inflexibility: The unavoidable biases of a public debate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3036-3054.
    16. Gambaro, Joao Paulo & Crokidakis, Nuno, 2017. "The influence of contrarians in the dynamics of opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 465-472.
    17. Sven Banisch, 2014. "From Microscopic Heterogeneity To Macroscopic Complexity In The Contrarian Voter Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-30.
    18. André C. R. Martins & Cleber D. Kuba, 2010. "The Importance Of Disagreeing: Contrarians And Extremism In The Coda Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 621-634.
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    2. Evangelos Ioannidis & Nikos Varsakelis & Ioannis Antoniou, 2020. "Promoters versus Adversaries of Change: Agent-Based Modeling of Organizational Conflict in Co-Evolving Networks," Mathematics, MDPI, vol. 8(12), pages 1-25, December.
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