On periodical behaviour in societies with symmetric influences

Abstract

We propose a simple model of society with a symmetric functionw(u, v) measuring the influence of the opinion of memberv on that of memberu. The opinions are chosen from a finite set. At each step everyone accepts the majority opinion (with respect tow) of the other members. The behaviour of such a society is clearly periodic after some initial time. We prove that the length of the period is either one or two.

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Poljak, S., Sůra, M. On periodical behaviour in societies with symmetric influences. Combinatorica 3, 119–121 (1983). https://doi.org/10.1007/BF02579347

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AMS subject classification (1980)

  • 90 A 08