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A Laplacian approach to stubborn agents and their role in opinion formation on influence networks

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  • Baumann, Fabian
  • Sokolov, Igor M.
  • Tyloo, Melvyn

Abstract

Within the framework of a simple model for social influence, the Taylor model, we analytically investigate the role of stubborn agents in the overall opinion dynamics of networked systems. Similar to zealots, stubborn agents are biased towards a certain opinion and have a major effect on the collective opinion formation process. Based on a modified version of the network Laplacian we derive quantities capturing the transient dynamics of the system and the emerging stationary opinion states. In the case of a single stubborn agent we characterize his/her ability to coherently change a prevailing consensus. For two antagonistic stubborn agents we investigate the opinion heterogeneity of the emerging non-consensus states and describe their statistical properties using a graph metric similar to the resistance distance in electrical networks. Applying the model to synthetic and empirical networks we find while opinion diversity is decreased by small-worldness and favored in the case of a pronounced community structure the opposite is true for the coherence of opinions during a consensus change.

Suggested Citation

  • Baumann, Fabian & Sokolov, Igor M. & Tyloo, Melvyn, 2020. "A Laplacian approach to stubborn agents and their role in opinion formation on influence networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    • Handle: RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304507
    DOI: 10.1016/j.physa.2020.124869
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    References listed on IDEAS

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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. Takasumi Kurahashi-Nakamura & Michael Mäs & Jan Lorenz, 2016. "Robust Clustering in Generalized Bounded Confidence Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 19(4), pages 1-7.
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    4. Dustin L. Arendt & Leslie M. Blaha, 2015. "Opinions, influence, and zealotry: a computational study on stubbornness," Computational and Mathematical Organization Theory, Springer, vol. 21(2), pages 184-209, June.
    5. 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.
    6. Guillaume Deffuant & David Neau & Frederic Amblard & Gérard Weisbuch, 2000. "Mixing beliefs among interacting agents," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 87-98.
    7. 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. Huang, Changwei & Hou, Yongzhao & Han, Wenchen, 2023. "Coevolution of consensus and cooperation in evolutionary Hegselmann–Krause dilemma with the cooperation cost," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Nikolaj Horsevad & David Mateo & Robert E. Kooij & Alain Barrat & Roland Bouffanais, 2022. "Transition from simple to complex contagion in collective decision-making," Nature Communications, Nature, vol. 13(1), pages 1-10, December.

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