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An analytical formulation for multidimensional continuous opinion models

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  • Pedraza, Lucía
  • Pinasco, Juan Pablo
  • Saintier, Nicolas
  • Balenzuela, Pablo

Abstract

Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions on different topics and therefore n-dimensional models are best suited to deal with these cases. While there have been many efforts to develop analytical models for one dimensional opinion models, less attention has been paid to multidimensional ones. In this work, we develop an analytical approach for multidimensional models of continuous opinions. We show that for any generic reciprocal interactions between agents, the mean value of initial opinion distribution is conserved. Moreover, for positive social influence interaction mechanisms, the variance of opinion distributions decreases with time and the system converges to a delta distributed function. In particular, we calculate the convergence time when agents get closer in a discrete quantity after interacting, showing a clear difference between cases where the approach is through Manhattan or Euclidean distance.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007220
    DOI: 10.1016/j.chaos.2021.111368
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    1. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    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. Laguna, M.F. & Abramson, Guillermo & Zanette, Damián H., 2003. "Vector opinion dynamics in a model for social influence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(3), pages 459-472.
    5. Amblard, Frédéric & Deffuant, Guillaume, 2004. "The role of network topology on extremism propagation with the relative agreement opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 725-738.
    6. Stefan Krasa & Mattias Polborn, 2014. "Policy Divergence and Voter Polarization in a Structural Model of Elections," Journal of Law and Economics, University of Chicago Press, vol. 57(1), pages 31-76.
    7. 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.
    8. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
    9. 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.
    10. 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.
    11. S. Huet & G. Deffuant & W. Jager, 2008. "A Rejection Mechanism In 2d Bounded Confidence Provides More Conformity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 529-549.
    12. 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:

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    3. Ni, Xuelian & Xiong, Fei & Pan, Shirui & Chen, Hongshu & Wu, Jia & Wang, Liang, 2023. "How heterogeneous social influence acts on human decision-making in online social networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Ding, Haixin & Xie, Li, 2024. "The applicability of positive information in negative opinion management: An attitude-laden communication perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).

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