Dynamics of Majority Rule

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

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• Opinion evolution in closed community
• Application of Statistical Physics to Politics
• Freezing in Ising Ferromagnets
• Domain Statistics in Coarsening Systems
• Metastable States in Spin Glasses and Disordered Ferromagnets

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