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We study consensus formation in interacting systems that evolve bymulti-state majority rule and by plurality rule. In an update event, a group ofG agents (with G odd), each endowed with an s-state spin variable, isspecified. For majority rule, all group members adopt the local majority state;for plurality rule the group adopts the local plurality state. This update isrepeated until a final consensus state is generally reached. In the mean fieldlimit, the consensus time for an N-spin system increases as ln N for bothmajority and plurality rule, with an amplitude that depends on s and G. Forfinite spatial dimensions, domains undergo diffusive coarsening in majorityrule when s or G is small. For larger s and G, opinions spread ballisticallyfrom the few groups with an initial local majority. For plurality rule, thereis always diffusive domain coarsening toward consensus.Comment: 8 pages, 11 figures, 2-column revtex4 format. Updated version: small  changes in response to referee comments. For publication in J Phys

Consensus formation in multi-state majority and plurality models