Dynamics of Majority Rule

Details Dynamics of Majority Rule Dynamics of Majority Rule

2003-03-11

arxiv.org/abs/cond-mat/0303182v3

Phys. Rev. Lett. 90, 238701 (2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in Eq.(1); a similar typo fixed in Eq.(6) and some references

Scientific paper

10.1103/PhysRevLett.90.238701

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.

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