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Effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics

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  • Balankin, Alexander S.
  • Martínez Cruz, Miguel Ángel
  • Martínez, Alfredo Trejo
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    Abstract

    We analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three-state square lattice divided into spatial cells (districts). In the spirit of the statistical mechanics of social impact, we introduce a dominant influence rule (DIR), according to which, in a single update step, a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres. In contrast to models based on some form of majority rule (MR), a system governed by the DIR is easily trapped in a stable non-consensus state, if all nodes of the discussion group have the same weight of influence. To ensure that a consensus in the DIR system is necessarily reached, we need to put a stochastic process in the update rule. Further, the stochastic DIR model is used as a starting point for understanding the effect of spatial heterogeneity of active agent (non-zero spin) distribution on the exit probabilities. Initially, the positive and negative spins (active agents) are assigned to some nodes with non-uniform spatial distributions; while the rest of the nodes remain in the state with spin zero (uncommitted voters). By varying the relative means and skewness of the initial spin distributions, we observe critical behaviors of exit probabilities in finite size systems. The critical exponents are obtained by Monte Carlo simulations. The results of numerical simulations are discussed in the context of social dynamics.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 390 (2011)
    Issue (Month): 21 ()
    Pages: 3876-3887

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    Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3876-3887

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Sociophysics; Monte Carlo simulation; Finite-size scaling; Critical exponents;

    References

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    1. Pabjan, Barbara & Pękalski, Andrzej, 2008. "Model of opinion forming and voting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6183-6189.
    2. Galam, Serge & Chopard, Bastien & Droz, Michel, 2002. "Killer geometries in competing species dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 256-263.
    3. Callander, Steven, 2008. "Majority rule when voters like to win," Games and Economic Behavior, Elsevier, vol. 64(2), pages 393-420, November.
    4. Lima, F.W.S. & Sousa, A.O. & Sumuor, M.A., 2008. "Majority-vote on directed Erdős–Rényi random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3503-3510.
    5. Vilela, André L.M. & Moreira, F.G. Brady, 2009. "Majority-vote model with different agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4171-4178.
    6. Galam, Serge, 2004. "The dynamics of minority opinions in democratic debate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 56-62.
    7. Ding, Fei & Liu, Yun & Shen, Bo & Si, Xia-Meng, 2010. "An evolutionary game theory model of binary opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1745-1752.
    8. Melatagia Yonta, Paulin & Ndoundam, René, 2009. "Opinion dynamics using majority functions," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 223-244, March.
    9. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 2.
    10. Galam, Serge, 1999. "Application of statistical physics to politics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 132-139.
    11. C. J. Tessone & R. Toral, 2004. "Neighborhood models of minority opinion spreading," Computing in Economics and Finance 2004 206, Society for Computational Economics.
    12. 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.
    13. Huang, Gan & Cao, Jinde & Wang, Guanjun & Qu, Yuzhong, 2008. "The strength of the minority," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4665-4672.
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