Dynamics of Majority Rule
Abstract
We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly-selected agents, consensus is reached in a time that scales ln N, where N is the number of agents. On finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.
Cite
@article{arxiv.cond-mat/0303182,
title = {Dynamics of Majority Rule},
author = {P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/0303182},
year = {2009}
}
Comments
4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in Eq.(1); a similar typo fixed in Eq.(6) and some references updates