Abstract
In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics the dependence of the consensus time on the population size exhibits two regimes. This is determined by the size distribution of the groups that, at each evolution step, gather to reach agreement. When the group size distribution has a finite mean value, the previously known logarithmic dependence on the population size holds. On the other hand, when the mean group size diverges, the consensus time and the population size are related through a power law. Numerical simulations validate this semi-quantitative analytical prediction.Received: 6 July 2009, Accepted: 2 September 2009; Edited by: M. C. Barbosa; Reviewed by: H. Fort, Universidad de la República, Uruguay; DOI: 10.4279/PIP.010002
Highlights
In this work, it is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes
Many of them are adaptations of well-known models for coarsening in interacting spin systems, whose dynamical rules are reinterpreted in the framework of social-like phenomena
It is found that the growth of the consensus time with the population size shows
Summary
It is pointed out that in the mean-field version of majority-rule opinion dynamics, the dependence of the consensus time on the population size exhibits two regimes. Consensus in a large population is reached by accumulative agreement events, each of them involving just a group of agents. The present note is aimed at briefly revisiting previous results on the time needed to reach consensus in majority-rule dynamics, stressing the role of the size distribution of the involved groups.
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