Majority Rule Dynamics

Opinion dynamics on a grid — consensus, disorder, and the noise threshold

0.020
4-cell
5
Opinion A: 50% Opinion B: 50% Step: 0 Order: 0.00
Each agent adopts the opinion of the local majority among its neighbors. With low noise, the system orders into domains. Above a critical noise threshold, thermal fluctuations destroy long-range order. This mirrors the Ising model: noise ↔ temperature, with a phase transition between ordered (consensus) and disordered (mixed) phases. Larger neighborhoods raise the critical noise.