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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References
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F. S. Roberts,Discrete Mathematical Models, with Application to Social, Biological, and Environmental Problems, Prentice-Hall, Englewood Cliffs, N. J. 1976.
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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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DOI: https://doi.org/10.1007/BF02579347