Consensus Formation in Multi-state Majority and Plurality Models

Details Consensus Formation in Multi-state Majority and Plurality Models Consensus Formation in Multi-state Majority and Plurality Models

2005-06-02

arxiv.org/abs/cond-mat/0506068v2

J. Phy. A 38, 7239-7252 (2005).

Physics

Condensed Matter

Statistical Mechanics

8 pages, 11 figures, 2-column revtex4 format. Updated version: small changes in response to referee comments. For publication

Scientific paper

10.1088/0305-4470/38/33/003

We study consensus formation in interacting systems that evolve by multi-state majority rule and by plurality rule. In an update event, a group of G agents (with G odd), each endowed with an s-state spin variable, is specified. For majority rule, all group members adopt the local majority state; for plurality rule the group adopts the local plurality state. This update is repeated until a final consensus state is generally reached. In the mean field limit, the consensus time for an N-spin system increases as ln N for both majority and plurality rule, with an amplitude that depends on s and G. For finite spatial dimensions, domains undergo diffusive coarsening in majority rule when s or G is small. For larger s and G, opinions spread ballistically from the few groups with an initial local majority. For plurality rule, there is always diffusive domain coarsening toward consensus.

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