Abstract
We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability For group size there is a phase transition at in all spatial dimensions. For the global majority quickly predominates, while for the system is driven to a mixed state in which the densities of agents in each state are equal. For the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a nontrivial dependence on the initial magnetization for all in agreement with numerical results. At the exact two-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.
- Received 4 June 2003
DOI:https://doi.org/10.1103/PhysRevE.68.046106
©2003 American Physical Society