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Theory of collective opinion shifts: from smooth trends to abrupt swings

Author

Listed:
  • Quentin Michard

    (CEA Saclay, Service de Physique de l’Etat Condensé)

  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

Abstract

We unveil collective effects induced by imitation and social pressure by analyzing data from three different sources: birth rates, sales of cell phones and the drop of applause in concert halls. We interpret our results within the framework of the Random Field Ising Model, which is a threshold model for collective decisions accounting both for agent heterogeneity and social imitation. Changes of opinion can occur either abruptly or continuously, depending on the importance of herding effects. The main prediction of the model is a scaling relation between the height h of the speed of variation peak and its width $w$ of the form h ~ w^{-kappa}, with kappa = 2/3 for well connected populations. Our three sets of data are compatible with such a prediction, with kappa ~ 0.62 for birth rates, kappa ~ 0.71 for cell phones and kappa ~ 0.64 for clapping. In this last case, we in fact observe that some clapping samples end discontinuously (w=0), as predicted by the model for strong enough imitation.

Suggested Citation

  • Quentin Michard & Jean-Philippe Bouchaud, 2005. "Theory of collective opinion shifts: from smooth trends to abrupt swings," Science & Finance (CFM) working paper archive 500060, Science & Finance, Capital Fund Management.
    • Handle: RePEc:sfi:sfiwpa:500060
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    Cited by:

    1. Christoph J. Borner & Ingo Hoffmann & John H. Stiebel, 2024. "A closer look at the chemical potential of an ideal agent system," Papers 2401.09233, arXiv.org.
    2. Vaz Martins, Teresa & Araújo, Tanya & Augusta Santos, Maria & St Aubyn, Miguel, 2009. "Network effects in a human capital based economic growth model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2207-2214.
    3. Denis Phan, 2006. "Discrete Choices under Social Influence:Generic Properties," Post-Print halshs-00105857, HAL.
    4. Sebastien Valeyre, 2022. "Optimal trend following portfolios," Papers 2201.06635, arXiv.org.
    5. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2012. "Entanglement between Demand and Supply in Markets with Bandwagon Goods," Papers 1209.1321, arXiv.org, revised Dec 2012.
    6. Serge Galam, 2011. "Market efficiency, anticipation and the formation of bubbles-crashes," Papers 1106.1577, arXiv.org.
    7. Damien Challet, 2016. "Regrets, learning and wisdom," Post-Print hal-01312973, HAL.
    8. Li, Jie & Wang, Juan & Sun, Shiwen & Xia, Chengyi, 2018. "Cascading crashes induced by the individual heterogeneity in complex networks," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 182-192.
    9. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    10. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    11. Christian Borghesi & Jean-Philippe Bouchaud, 2007. "Of songs and men: a model for multiple choice with herding," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 557-568, August.
    12. Martins, André C.R. & Pereira, Carlos de B. & Vicente, Renato, 2009. "An opinion dynamics model for the diffusion of innovations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3225-3232.
    13. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers 1209.0453, arXiv.org, revised Dec 2012.
    14. Kindler, A. & Solomon, S. & Stauffer, D., 2013. "Peer-to-peer and mass communication effect on opinion shifts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 785-796.
    15. Daniele Notarmuzi & Claudio Castellano & Alessandro Flammini & Dario Mazzilli & Filippo Radicchi, 2022. "Universality, criticality and complexity of information propagation in social media," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    16. Sebastien Valeyre, 2020. "Refined model of the covariance/correlation matrix between securities," Papers 2001.08911, arXiv.org.
    17. Jean Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Post-Print hal-04145594, HAL.
    18. Moran, José & Fosset, Antoine & Kirman, Alan & Benzaquen, Michael, 2021. "From ants to fishing vessels: a simple model for herding and exploitation of finite resources," Journal of Economic Dynamics and Control, Elsevier, vol. 129(C).
    19. Thompson, Michael & Young, Louise, 2014. "Measuring complex patterns in space–time," Australasian marketing journal, Elsevier, vol. 22(1), pages 28-35.
    20. Jean-Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Papers 2306.16165, arXiv.org.

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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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