Dynamics of Majority Rule in Two-State Interacting Spin Systems

TLDR

The model introduces a two‑state opinion dynamics framework driven by majority rule. Updates are performed by selecting a group of agents and having all members adopt the local majority state. In mean‑field the consensus time scales as ln N, whereas on finite lattices it fluctuates and grows as a dimension‑dependent power of N, with an upper critical dimension above 4, and the final opinion equals the initial majority except in one dimension.

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.