IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v572y2021ics0378437121001746.html
   My bibliography  Save this article

Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases

Author

Listed:
  • Khalil, Nagi

Abstract

A model for continuous-opinion dynamics is proposed and studied by taking advantage of its similarities with a mono-dimensional granular gas. Agents interact as in the Deffuant model, with a parameter α controlling the persuasibility of the individuals. The interaction coincides with the collision rule of two grains moving on a line, provided opinions and velocities are identified, with α being the so-called coefficient of normal restitution. Starting from the master equation of the probability density of all opinions, general conditions are given for the system to reach consensus. The case when the interaction frequency is proportional to the β-power of the relative opinions is studied in more detail. It is shown that the mean-field approximation to the master equation leads to the Boltzmann kinetic equation for the opinion distribution. In this case, the system always approaches consensus, which can be seen as the approach to zero of the opinion temperature, a measure of the width of the opinion distribution. Moreover, the long-time behaviour of the system is characterized by a scaling solution to the Boltzmann equation in which all time dependence occurs through the temperature. The case β=0 is related to the Deffuant model and is analytically soluble. The scaling distribution is unimodal and independent of α. For β>0 the distribution of opinions is unimodal below a critical value of |α|, being multimodal with two maxima above it. This means that agents may approach consensus while being polarized. Near the critical points and for |α|≥0.4, the distribution of opinions is well approximated by the sum of two Gaussian distributions. Monte Carlo simulations are in agreement with the theoretical results.

Suggested Citation

  • Khalil, Nagi, 2021. "Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    • Handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001746
    DOI: 10.1016/j.physa.2021.125902
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121001746
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2021.125902?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    4. Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    5. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
    6. Jan Lorenz, 2007. "Continuous Opinion Dynamics Under Bounded Confidence: A Survey," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(12), pages 1819-1838.
    7. C. Borghesi & J.-P. Bouchaud, 2010. "Spatial correlations in vote statistics: a diffusive field model for decision-making," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 75(3), pages 395-404, June.
    8. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
    9. Granovsky, Boris L. & Madras, Neal, 1995. "The noisy voter model," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 23-43, January.
    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. Noije, T.P.C.van & Ernst, M.H. & Brito, R., 1998. "Ring kinetic theory for an idealized granular gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 251(1), pages 266-283.
    12. Andreas Flache & Michael Mäs & Thomas Feliciani & Edmund Chattoe-Brown & Guillaume Deffuant & Sylvie Huet & Jan Lorenz, 2017. "Models of Social Influence: Towards the Next Frontiers," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 20(4), pages 1-2.
    13. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Griffin, Christopher & Squicciarini, Anna & Jia, Feiran, 2022. "Consensus in complex networks with noisy agents and peer pressure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    2. Aguilar-Janita, Miguel & Blanco-Alonso, Andres & Khalil, Nagi, 2024. "Polarization-induced stress in the noisy voter model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 647(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Guillaume Deffuant & Ilaria Bertazzi & Sylvie Huet, 2018. "The Dark Side Of Gossips: Hints From A Simple Opinion Dynamics Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-20, September.
    3. G Jordan Maclay & Moody Ahmad, 2021. "An agent based force vector model of social influence that predicts strong polarization in a connected world," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-42, November.
    4. Weimer, Christopher W. & Miller, J.O. & Hill, Raymond R. & Hodson, Douglas D., 2022. "An opinion dynamics model of meta-contrast with continuous social influence forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. Takesue, Hirofumi, 2023. "Relative opinion similarity leads to the emergence of large clusters in opinion formation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    6. Luo, Yun & Li, Yuke & Sun, Chudi & Cheng, Chun, 2022. "Adapted Deffuant–Weisbuch model with implicit and explicit opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    7. Christos Mavridis & Nikolas Tsakas, 2021. "Social Capital, Communication Channels and Opinion Formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 635-678, May.
    8. Francisco J. León-Medina & Jordi Tena-Sánchez & Francisco J. Miguel, 2020. "Fakers becoming believers: how opinion dynamics are shaped by preference falsification, impression management and coherence heuristics," Quality & Quantity: International Journal of Methodology, Springer, vol. 54(2), pages 385-412, April.
    9. Peralta, Antonio F. & Khalil, Nagi & Toral, Raúl, 2020. "Ordering dynamics in the voter model with aging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    10. Lipiecki, Arkadiusz & Sznajd-Weron, Katarzyna, 2022. "Polarization in the three-state q-voter model with anticonformity and bounded confidence," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    11. Kononovicius, Aleksejus, 2021. "Supportive interactions in the noisy voter model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Antonio Parravano & Ascensión Andina-Díaz & Miguel A Meléndez-Jiménez, 2016. "Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-23, October.
    13. Deffuant, Guillaume & Roubin, Thibaut, 2023. "Emergence of group hierarchy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    14. Sylvie Huet & Jean-Denis Mathias, 2018. "Few Self-Involved Agents Among Bounded Confidence Agents Can Change Norms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 21(06n07), pages 1-27, September.
    15. Deffuant, Guillaume & Roubin, Thibaut, 2022. "Do interactions among unequal agents undermine those of low status?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    16. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    17. Li, Mingwu & Dankowicz, Harry, 2019. "Impact of temporal network structures on the speed of consensus formation in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1355-1370.
    18. Shane T. Mueller & Yin-Yin Sarah Tan, 2018. "Cognitive perspectives on opinion dynamics: the role of knowledge in consensus formation, opinion divergence, and group polarization," Journal of Computational Social Science, Springer, vol. 1(1), pages 15-48, January.
    19. 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).
    20. Castro, Luis E. & Shaikh, Nazrul I., 2018. "A particle-learning-based approach to estimate the influence matrix of online social networks," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 1-18.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:572:y:2021:i:c:s0378437121001746. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.