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Unity and discord in opinion dynamics

Author

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  • Ben-Naim, E
  • Krapivsky, P.L
  • Vazquez, F
  • Redner, S

Abstract

We study opinion dynamics models where agents evolve via repeated pairwise interactions. In the compromise model, agents with sufficiently close real-valued opinions average their opinions. A steady state is reached with a finite number of isolated, noninteracting opinion clusters (“parties”). As the initial opinion range increases, the number of such parties undergoes a periodic bifurcation sequence, with alternating major and minor parties. In the constrained voter model, there are leftists, centrists, and rightists. A centrist and an extremist can both become centrists or extremists in an interaction, while leftists and rightists do not affect each other. The final state is either consensus or a frozen population of leftists and rightists. The evolution in one dimension is mapped onto a constrained spin-1 Ising chain with zero-temperature Glauber kinetics. The approach to the final state exhibits a nonuniversal long-time tail.

Suggested Citation

  • Ben-Naim, E & Krapivsky, P.L & Vazquez, F & Redner, S, 2003. "Unity and discord in opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 99-106.
    • Handle: RePEc:eee:phsmap:v:330:y:2003:i:1:p:99-106
    DOI: 10.1016/j.physa.2003.08.027
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    Citations

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    Cited by:

    1. Bertotti, Maria Letizia & Modanese, Giovanni, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3782-3793.
    2. Sylvie Huet & Margaret Edwards & Guillaume Deffuant, 2007. "Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(1), pages 1-10.
    3. Grabowski, Andrzej, 2009. "Opinion formation in a social network: The role of human activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 961-966.
    4. Diemo Urbig & Jan Lorenz & Heiko Herzberg, 2008. "Opinion Dynamics: the Effect of the Number of Peers Met at Once," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-4.
    5. Hendrickx, Julien M., 2008. "Order preservation in a generalized version of Krause’s opinion dynamics model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5255-5262.
    6. Liang, Haili & Yang, Yiping & Wang, Xiaofan, 2013. "Opinion dynamics in networks with heterogeneous confidence and influence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2248-2256.
    7. Boudin, Laurent & Mercier, Aurore & Salvarani, Francesco, 2012. "Conciliatory and contradictory dynamics in opinion formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5672-5684.
    8. Gualandi, Stefano & Toscani, Giuseppe, 2017. "Pareto tails in socio-economic phenomena: A kinetic description," Economics Discussion Papers 2017-111, Kiel Institute for the World Economy (IfW Kiel).
    9. Maria Letizia Bertotti & Giovanni Modanese, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Papers 1109.0606, arXiv.org.
    10. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    11. Boudin, Laurent & Salvarani, Francesco, 2016. "Opinion dynamics: Kinetic modelling with mass media, application to the Scottish independence referendum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 448-457.
    12. Grabowski, A. & Kosiński, R.A., 2006. "Ising-based model of opinion formation in a complex network of interpersonal interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(2), pages 651-664.

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