title: Dynamics of majority rule in two-state interacting spin systems.
abstract: We introduce a two-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.
authors.affiliation: Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, MA 02215, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
authors.forename: S
authors.initials: S
authors.lastname: Redner