Type
Article
Titre
Testing the validity of the Kirkwood approximation using an extended Sznajd model
Dans
Physical Review E
Auteur(s)
TIMPANARO André - Instituto de Fisica [São Paulo] (Auteur)
GALAM Serge - Centre de recherches politiques de Sciences Po (Auteur)
Éditeur
US
Volume
92
Numéro
6
Pages
1 - 6 p.
ISSN
15393755
Mots clés
Sociophysics, Opinion dynamics, Kirkwood approximation, Sznajd model
Résumé
EN
We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008)]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008); R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008); A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014)], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and “United we stand, divided we fall” models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975); K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000)] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with 103 sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability.

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