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Modeling opinion dynamics: Theoretical analysis and continuous approximation

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  • Pinasco, Juan Pablo
  • Semeshenko, Viktoriya
  • Balenzuela, Pablo

Abstract

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion and the agreement is reached because the new arguments are incorporated. Given the wide range of opinion formation mathematical approaches, there are however no models of opinion dynamics with nonlocal pair interactions analytically solvable. In this paper we present a novel analytical framework developed to solve the master equations with non-local kernels. For this we used a simple model of opinion formation where individuals tend to get more similar after each interactions, no matter their opinion differences, giving rise to nonlinear differential master equation with non-local terms. Simulation results show an excellent agreement with results obtained by the theoretical estimation.

Suggested Citation

  • Pinasco, Juan Pablo & Semeshenko, Viktoriya & Balenzuela, Pablo, 2017. "Modeling opinion dynamics: Theoretical analysis and continuous approximation," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 210-215.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:210-215
    DOI: 10.1016/j.chaos.2017.03.033
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    References listed on IDEAS

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    1. Pablo Balenzuela & Juan Pablo Pinasco & Viktoriya Semeshenko, 2015. "The Undecided Have the Key: Interaction-Driven Opinion Dynamics in a Three State Model," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-21, October.
    2. 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.
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    Cited by:

    1. Pedraza, Lucía & Pinasco, Juan Pablo & Semeshenko, Viktoriya & Balenzuela, Pablo, 2023. "Mesoscopic analytical approach in a three state opinion model with continuous internal variable," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Qesmi, Redouane, 2021. "Hopf bifurcation in an opinion model with state-dependent delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Thomas Feliciani & Andreas Flache & Michael Mäs, 2021. "Persuasion without polarization? Modelling persuasive argument communication in teams with strong faultlines," Computational and Mathematical Organization Theory, Springer, vol. 27(1), pages 61-92, March.
    4. Pedraza, Lucía & Pinasco, Juan Pablo & Saintier, Nicolas & Balenzuela, Pablo, 2021. "An analytical formulation for multidimensional continuous opinion models," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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