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Approaching consensus can be delicate when positions harden

Author

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  • Cohen, Joel E.
  • Hajnal, John
  • Newman, Charles M.

Abstract

A model of consensus leads to examples in which the ergodic behavior of a nonstationary product of random nonnegative matrices depends discontinuously on a continuous parameter. In these examples, a product of random matrices, each of which is a scrambling stochastic matrix, changes from being weakly ergodic (asymptotically of rank 1) with probability 1 to being weakly ergodic with probability 0 as a parameter of the process changes smoothly.

Suggested Citation

  • Cohen, Joel E. & Hajnal, John & Newman, Charles M., 1986. "Approaching consensus can be delicate when positions harden," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 315-322, July.
    • Handle: RePEc:eee:spapps:v:22:y:1986:i:2:p:315-322
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    Cited by:

    1. Dimitris Tsintsaris & Milan Tsompanoglou & Evangelos Ioannidis, 2024. "Dynamics of Social Influence and Knowledge in Networks: Sociophysics Models and Applications in Social Trading, Behavioral Finance and Business," Mathematics, MDPI, vol. 12(8), pages 1-27, April.
    2. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    3. Kevin JS. Zollman, 2012. "Social network structure and the achievement of consensus," Politics, Philosophy & Economics, , vol. 11(1), pages 26-44, February.
    4. Gérard Weisbuch & Guillaume Deffuant & Frederic Amblard & Jean Pierre Nadal, 2001. "Interacting Agents and Continuous Opinions Dynamics," Working Papers 01-11-072, Santa Fe Institute.
    5. Gazon, Jules, 2008. "Collective opinion formation of individuals socially embedded in a power structure," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(1), pages 108-137, February.
    6. Verma, Gunjan & Swami, Ananthram & Chan, Kevin, 2014. "The impact of competing zealots on opinion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 310-331.

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