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

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  • Quentin Michard

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

  • Jean-Philippe Bouchaud

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

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    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.

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    Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500060.

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    Date of creation: Apr 2005
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    Handle: RePEc:sfi:sfiwpa:500060

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    Cited by:
    1. Teresa Vaz Martins & Tanya Araujo & Maria Augusta Santos & Miguel St Aubyn, 2008. "Network effects in a human capital based economic growth model," Papers, arXiv.org 0809.3418, arXiv.org, revised Feb 2009.
    2. 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, Elsevier, vol. 388(15), pages 3225-3232.
    3. 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, Elsevier, vol. 392(4), pages 785-796.
    4. Jean-Philippe Bouchaud, 2012. "Crises and collective socio-economic phenomena: simple models and challenges," Papers, arXiv.org 1209.0453, arXiv.org, revised Dec 2012.
    5. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank, European Central Bank.
    6. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2012. "Entanglement between Demand and Supply in Markets with Bandwagon Goods," Papers, arXiv.org 1209.1321, arXiv.org, revised Dec 2012.
    7. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers, arXiv.org 1404.0243, arXiv.org.

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