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Dynamics Analysis for the Random Homogeneous Biased Assimilation Model

Author

Listed:
  • Jiangbo Zhang

    (School of Science, Southwest Petroleum University, Chengdu 610500, China)

  • Yiyi Zhao

    (School of Business Administration, Faculty of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China)

Abstract

This paper studies the evolution of opinions over random social networks subject to individual biases. An agent reviews the opinion of a randomly selected one and then updates its opinion under homogeneous biased assimilation. This study investigates the impact of biased assimilation on random opinion networks, which is different from the previous studies on fixed network structures. If the bias parameters are static, it is proven that the event in which all agents converge to extreme opinions happens almost surely. Next, the opinion polarization event is proved to be a probability one event. While if the bias parameters are dynamic, the opinion evolution is proven to depend on early finite time slots for the dynamical individual bias parameter functions independent of the biased parameter values after the time threshold. Numerical simulations further show that opinion evolution depends on early finite time slots for some nonlinear dynamical individual bias parameter functions.

Suggested Citation

  • Jiangbo Zhang & Yiyi Zhao, 2023. "Dynamics Analysis for the Random Homogeneous Biased Assimilation Model," Mathematics, MDPI, vol. 11(7), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1661-:d:1111826
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    References listed on IDEAS

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    1. Isaac Waller & Ashton Anderson, 2021. "Quantifying social organization and political polarization in online platforms," Nature, Nature, vol. 600(7888), pages 264-268, December.
    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. Daron Acemoğlu & Giacomo Como & Fabio Fagnani & Asuman Ozdaglar, 2013. "Opinion Fluctuations and Disagreement in Social Networks," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 1-27, February.
    4. Guodong Shi & Alexandre Proutiere & Mikael Johansson & John S. Baras & Karl H. Johansson, 2016. "The Evolution of Beliefs over Signed Social Networks," Operations Research, INFORMS, vol. 64(3), pages 585-604, June.
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