A note on the consensus time of mean-field majority-rule dynamics

Details A note on the consensus time of mean-field majority-rule dynamics A note on the consensus time of mean-field majority-rule dynamics

2009-09-11

arxiv.org/abs/0909.2246v2

Pap. Phys. 1, 010002 (2009)

Physics

Physics and Society

4 pages, 3 figures, Commentary and Reply available in Papers in Physics

Scientific paper

10.4279/pip.010002

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.

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