Consensus Formation in Multi-state Majority and Plurality Models

Abstract

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.

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

References in corpus (4)

• Opinion evolution in closed community
• Dynamics of Majority Rule
• Freezing in Ising Ferromagnets
• Majority Rule Dynamics in Finite Dimensions

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• Finite-size effects on the convergence time in continuous-opinion dynamics
• Social dynamics with peer support on heterogeneous networks: The "mafia model"
• Phase Transitions in Biased Opinion Dynamics with 2-choices Rule