Dynamics of Majority Rule
arXiv:cond-mat/0303182 · doi:10.1103/PhysRevLett.90.238701
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.
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