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Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics pp 174–185Cite as

Opinion Network Modeling and Experiment

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Part of the book series: Understanding Complex Systems ((UCS))

Abstract

We present a model describing the temporal evolution of opinions due to interactions among a network of individuals. This Accept-Shift-Constrict (ASC) model is formulated in terms of coupled nonlinear differential equations for opinions and uncertainties. The ASC model dynamics allows for the emergence and persistence of majority positions so that the mean opinion can shift even for a symmetric network. The model also formulates a distinction between opinion and rhetoric in accordance with a recently proposed theory of the group polarization effect. This enables the modeling of discussion-induced shifts toward the extreme without the typical modeling assumption of greater resistance to persuasion among extremists. An experiment is described in which triads engaged in online discussion. Simulations show that the ASC model is in qualitative and quantitative agreement with the experimental data.

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Notes

  1. 1.

    In actual practice, bets are returned if the victory margin equals the spread.

  2. 2.

    The persistence of majority positions on a continuous opinion axis is also found in the agent-based model of [16], which employs a confidence variable that must be transmitted between agents along with opinions, rather than the ASC model’s use of an uncertainty interval not visible to others.

  3. 3.

    The sum of the communication weights is normalized to the same (arbitrary) value of 3 in both networks, a value that only affects the transient time and not the final equilibrium.

  4. 4.

    If the subjective probability of one of the binary outcomes is taken as the rhetorical frame and opposing policy sides have opposite signs, then concavity with increasing policy extremity yields an overall S-shaped rhetorical function as explained in [12].

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Acknowledgements

This work was supported by the Office of Naval Research under grant N00014–15–1–2549.

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Authors and Affiliations

  1. Applied Physics Laboratory, University of Washington, 1013 NE 40th St, Seattle, WA, 98105-6698, USA

    Michael Gabbay

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  1. Michael Gabbay
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Correspondence to Michael Gabbay .

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Editors and Affiliations

  1. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Visarath In

  2. Space and Naval Warfare Systems Center, San Diego, CA, USA

    Patrick Longhini

  3. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Antonio Palacios

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Gabbay, M. (2019). Opinion Network Modeling and Experiment. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 5th International Conference on Applications in Nonlinear Dynamics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-10892-2_18

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  • DOI: https://doi.org/10.1007/978-3-030-10892-2_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10891-5

  • Online ISBN: 978-3-030-10892-2

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