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Majority Rule in Nonlinear Opinion Dynamics

  • Michael Gabbay
  • Arindam K. Das
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Using a nonlinear model of opinion dynamics on networks, we show the existence of asymmetric majority rule solutions for symmetric initial opinion distributions and symmetric network structure. We show that this occurs in triads as the result of a pitchfork bifurcation and arises in both chain and complete topologies with symmetric as well as asymmetric coupling. Analytical approximations for bifurcation boundaries are derived which closely match numerically-obtained boundaries. Bifurcation-induced symmetry breaking represents a novel mechanism for generating majority rule outcomes without built-in structural or dynamical asymmetries; however, the policy outcome is fundamentally unpredictable.

Keywords

Coupling Strength Majority Rule Center Node Chain Network Coupling Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We acknowledge the support of the Defense Threat Reduction Agency and the Office of Naval Research under grant HDTRA1-10-1-0075.

References

  1. 1.
    C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)CrossRefGoogle Scholar
  2. 2.
    J.H. Davis, Group decision making and quantitative judgments: a consensus model, in Understanding Group Behavior: Consensual Action by Small Groups, ed. by E. Witte, J.H. Davis (Lawrence Erlbaum, Mahwah, 1996)Google Scholar
  3. 3.
    A. Dhooge, W. Govaerts, Y.A. Kuznetsov, Matcont: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Softw. 29(2), 141–164 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    A. Eagly, S. Chaiken, The Psychology of Attitudes (Harcourt, Fort Worth, 1993)Google Scholar
  5. 5.
    N.E. Friedkin, E.C. Johnsen, Social Influence Network Theory: A Sociological Examination of Small Group Dynamics (Cambridge University Press, Cambridge, 2011)CrossRefGoogle Scholar
  6. 6.
    M. Gabbay, A dynamical systems model of small group decision making, in Diplomacy Games, ed. by R. Avenhaus, I.W. Zartman (Springer, Berlin, 2007)Google Scholar
  7. 7.
    M. Gabbay, The effects of nonlinear interactions and network structure in small group opinion dynamics. Phys. A Stat. Mech. Appl. 378(1), 118–126 (2007)Google Scholar
  8. 8.
    J. Gastil, The Group in Society (Sage, Los Angeles, 2010)Google Scholar
  9. 9.
    M. Hinich, M. Munger, Analytical Politics (Cambridge University Press, Cambridge, 1997)CrossRefGoogle Scholar
  10. 10.
    M. Mesbahi, M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (Princeton University Press, Princeton, 2010)zbMATHGoogle Scholar
  11. 11.
    V. Srivastava, J. Moehlis, F. Bullo, On bifurcations in nonlinear consensus networks. J. Nonlinear Sci. 21, 875–895 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    S.H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, Reading, 1994)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Applied Physics LaboratoryUniversity of WashingtonSeattleUSA
  2. 2.Department of Engineering and DesignEastern Washington UniversityCheneyUSA

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