IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-03573376.html
   My bibliography  Save this paper

The threshold model with anticonformity under random sequential updating

Author

Listed:
  • Bartłomiej Nowak

    (Wroclaw University of Science and Technology)

  • Michel Grabisch

    (UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Katarzyna Sznajd-Weron

    (Wroclaw University of Science and Technology)

Abstract

We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which the thresholds are given by a beta distribution parametrized by two positive shape parameters α and β. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass, arise only for values of α and β that yield the shape of the distribution observed in real social systems.

Suggested Citation

  • Bartłomiej Nowak & Michel Grabisch & Katarzyna Sznajd-Weron, 2022. "The threshold model with anticonformity under random sequential updating," Post-Print halshs-03573376, HAL.
  • Handle: RePEc:hal:journl:halshs-03573376
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03573376
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-03573376/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

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


    Cited by:

    1. Lee, Kyu-Min & Lee, Sungmin & Min, Byungjoon & Goh, K.-I., 2023. "Threshold cascade dynamics on signed random networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    More about this item

    Keywords

    opinion dynamics; threshold model; anticonformity; mean-field approximation; Markov chain; dynamique d'opinion; modèle à seuil; anti-conformisme; approximation à champ moyen; chaîne de Markov;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:journl:halshs-03573376. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.