IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v395y2014icp310-331.html
   My bibliography  Save this article

The impact of competing zealots on opinion dynamics

Author

Listed:
  • Verma, Gunjan
  • Swami, Ananthram
  • Chan, Kevin

Abstract

An individual’s opinion on an issue is greatly impacted by others in his or her social network. Most people are open-minded and ready to change their opinion when presented evidence; however, some are zealots or inflexibles, that is, individuals who refuse to change their opinion while staunchly advocating an opinion in hopes of convincing others. Zealotry is present in opinions of significant personal investment, such as political, religious or corporate affiliation; it tends to be less commonplace in opinions involving rumors or fashion trends. In this paper, we examine the effect that zealots have in a population whose opinion dynamics obey the naming game model. We present numerical and analytical results about the number and nature of steady state solutions, demonstrating the existence of a bifurcation in the space of zealot fractions. Our analysis indicates conditions under which a minority zealot opinion ultimately prevails, and conditions under which neither opinion attains a majority. We also present numerical and simulation analysis of finite populations and on networks with partial connectivity.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:395:y:2014:i:c:p:310-331
    DOI: 10.1016/j.physa.2013.09.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113009229
    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.2013.09.045?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. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
    2. Andrea Baronchelli & Vittorio Loreto & Luc Steels, 2008. "In-Depth Analysis Of The Naming Game Dynamics: The Homogeneous Mixing Case," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 785-812.
    3. Cohen, Joel E. & Hajnal, John & Newman, Charles M., 1986. "Approaching consensus can be delicate when positions harden," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 315-322, July.
    4. Galam, Serge & Jacobs, Frans, 2007. "The role of inflexible minorities in the breaking of democratic opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 366-376.
    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. X. Castelló & A. Baronchelli & V. Loreto, 2009. "Consensus and ordering in language dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 557-564, October.
    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. Luo, Gui-Xun & Liu, Yun & Zeng, Qing-An & Diao, Su-Meng & Xiong, Fei, 2014. "A dynamic evolution model of human opinion as affected by advertising," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 254-262.
    2. Han, Wenchen & Gao, Shun & Huang, Changwei & Yang, Junzhong, 2022. "Non-consensus states in circular opinion model with repulsive interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    3. 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).
    4. Li, Tingyu & Zhu, Hengmin, 2020. "Effect of the media on the opinion dynamics in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    5. Kalinowska, Zuzanna & Dybiec, Bartłomiej, 2023. "Weighted Axelrod model: Different but similar," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    6. Marco Mancastroppa & Iacopo Iacopini & Giovanni Petri & Alain Barrat, 2023. "Hyper-cores promote localization and efficient seeding in higher-order processes," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    7. Catherine A. Glass & David H. Glass, 2021. "Social Influence of Competing Groups and Leaders in Opinion Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 799-823, October.
    8. Zhou, Jianfeng & Lou, Yang & Chen, Guanrong & Tang, Wallace K.S., 2018. "Multi-language naming game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 620-634.
    9. Fudolig, Mikaela Irene D. & Esguerra, Jose Perico H., 2014. "Analytic treatment of consensus achievement in the single-type zealotry voter model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 626-634.

    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. Tiwari, Mukesh & Yang, Xiguang & Sen, Surajit, 2021. "Modeling the nonlinear effects of opinion kinematics in elections: A simple Ising model with random field based study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    2. Fan, Kangqi & Pedrycz, Witold, 2016. "Opinion evolution influenced by informed agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 431-441.
    3. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    4. Si, Xia-Meng & Liu, Yun & Xiong, Fei & Zhang, Yan-Chao & Ding, Fei & Cheng, Hui, 2010. "Effects of selective attention on continuous opinions and discrete decisions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3711-3719.
    5. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    6. Qian, Shen & Liu, Yijun & Galam, Serge, 2015. "Activeness as a key to counter democratic balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 187-196.
    7. Matjaž Steinbacher & Mitja Steinbacher, 2019. "Opinion Formation with Imperfect Agents as an Evolutionary Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 479-505, February.
    8. Fan, Kangqi & Pedrycz, Witold, 2015. "Emergence and spread of extremist opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 87-97.
    9. Balankin, Alexander S. & Martínez Cruz, Miguel Ángel & Martínez, Alfredo Trejo, 2011. "Effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3876-3887.
    10. Deng, Lei & Liu, Yun & Xiong, Fei, 2013. "An opinion diffusion model with clustered early adopters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3546-3554.
    11. Martins, André C.R., 2022. "Extremism definitions in opinion dynamics models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    12. Shang, Lihui & Zhao, Mingming & Ai, Jun & Su, Zhan, 2021. "Opinion evolution in the Sznajd model on interdependent chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    13. Lu, Xi & Mo, Hongming & Deng, Yong, 2015. "An evidential opinion dynamics model based on heterogeneous social influential power," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 98-107.
    14. Dimitris Tsintsaris & Milan Tsompanoglou & Evangelos Ioannidis, 2024. "Dynamics of Social Influence and Knowledge in Networks: Sociophysics Models and Applications in Social Trading, Behavioral Finance and Business," Mathematics, MDPI, vol. 12(8), pages 1-27, April.
    15. María Cecilia Gimenez & Luis Reinaudi & Ana Pamela Paz-García & Paulo Marcelo Centres & Antonio José Ramirez-Pastor, 2021. "Opinion evolution in the presence of constant propaganda: homogeneous and localized cases," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-11, January.
    16. Toth, Gabor & Galam, Serge, 2022. "Deviations from the majority: A local flip model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    17. Diao, Su-Meng & Liu, Yun & Zeng, Qing-An & Luo, Gui-Xun & Xiong, Fei, 2014. "A novel opinion dynamics model based on expanded observation ranges and individuals’ social influences in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 220-228.
    18. Si, Xia-Meng & Wang, Wen-Dong & Ma, Yan, 2016. "Role of propagation thresholds in sentiment-based model of opinion evolution with information diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 549-559.
    19. Song, Xiao & Shi, Wen & Tan, Gary & Ma, Yaofei, 2015. "Multi-level tolerance opinion dynamics in military command and control networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 322-332.
    20. Song, Xiao & Zhang, Shaoyun & Qian, Lidong, 2013. "Opinion dynamics in networked command and control organizations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5206-5217.

    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:395:y:2014:i:c:p:310-331. 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.