Brazilian Journal of Physics

, Volume 42, Issue 1–2, pp 125–131 | Cite as

Competition Among Reputations in the 2D Sznajd Model: Spontaneous Emergence of Democratic States



We propose a modification in the Sznajd sociophysics model defined on the square lattice. For this purpose, we consider reputation—a mechanism limiting the agents’ persuasive power. The reputation is introduced as a time-dependent score, which can be positive or negative. This mechanism avoids dictatorship (full consensus, all spins parallel) for a wide range of model parameters. We consider two different situations: case 1, in which the agents’ reputation increases for each persuaded neighbor, and case 2, in which the agents’ reputation increases for each persuasion and decreases when a neighbor keeps his opinion. Our results show that the introduction of reputation avoids full consensus even for initial densities of up spins greater than 1/2. The relaxation times follow a log-normal-like distribution in both cases, but they are larger in case 2 due to the competition among reputations. In addition, we show that the usual phase transition occurs and depends on the initial concentration d of individuals with the same opinion, but the critical points d c in the two cases are different.


Dynamics of social systems Phase transitions Cellular automata 



N. Crokidakis would like to thank the Brazilian funding agency CNPq for the financial support. Financial support from the Brazilian agency CAPES at Universidade de Aveiro at Portugal is also acknowledge. F. L. Forgerini would like to thank the ISB—Universidade Federal do Amazonas for the support.


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Copyright information

© Sociedade Brasileira de Física 2012

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal FluminenseNiteróiBrazil
  2. 2.Departamento de Física, I3NUniversidade de AveiroAveiroPortugal
  3. 3.ISBUniversidade Federal do AmazonasCoariBrazil

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