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The effects of nonlinear interactions and network structure in small group opinion dynamics

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  • Gabbay, Michael

Abstract

We present a model of opinion dynamics in social networks in which an individual's opinion evolves under the action of (i) a linear force which tends to restore the opinion back towards the individual's natural bias that is his or her initial opinion and (ii) a nonlinear coupling with other individuals which acts to bring opinions closer together but wanes for high opinion discrepancies. Bifurcation analysis for the case of a two-person group shows that a critical value for the difference in natural biases exists which demarcates regimes of qualitatively different behavior. For low to moderate natural bias differences, the dynamics are qualitatively similar to linear theory. For high bias differences, the system takes on a binary nature and is marked by discontinuous transitions between deadlock and consensus as well as hysteresis as the coupling is varied. The coupling required to force consensus grows extremely rapidly with the natural bias difference indicating that trying to achieve group consensus solely via increasing the communications rate becomes fruitless as the biases become extremely divergent. We also show that, for high bias differences, a triad broker network topology can reduce group discord more effectively than a clique, contrary to linear theory.

Suggested Citation

  • Gabbay, Michael, 2007. "The effects of nonlinear interactions and network structure in small group opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(1), pages 118-126.
    • Handle: RePEc:eee:phsmap:v:378:y:2007:i:1:p:118-126
    DOI: 10.1016/j.physa.2006.11.051
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    References listed on IDEAS

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    1. Guillaume Deffuant, 2006. "Comparing Extremism Propagation Patterns in Continuous Opinion Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(3), pages 1-8.
    2. 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 1-2.
    3. Guillaume Deffuant & Frederic Amblard & Gérard Weisbuch, 2002. "How Can Extremism Prevail? a Study Based on the Relative Agreement Interaction Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(4), pages 1-1.
    4. Laurent Salzarulo, 2006. "A Continuous Opinion Dynamics Model Based on the Principle of Meta-Contrast," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(1), pages 1-13.
    5. Weisbuch, Gérard & Deffuant, Guillaume & Amblard, Frédéric, 2005. "Persuasion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 555-575.
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    Cited by:

    1. Peter Kurrild-Klitgaard & Urs Steiner Brandt, 2021. "The calculus of democratic deliberation," Constitutional Political Economy, Springer, vol. 32(2), pages 165-186, June.
    2. Muhammad Umar B. Niazi & A. Bülent Özgüler, 2021. "A Differential Game Model of Opinion Dynamics: Accord and Discord as Nash Equilibria," Dynamic Games and Applications, Springer, vol. 11(1), pages 137-160, March.
    3. Weimer-Jehle, Wolfgang, 2008. "Cross-impact balances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3689-3700.

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