On periodical behaviour in societies with symmetric influences


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.

This is a preview of subscription content, access via your institution.


  1. [1]

    J. R. P. French, A Formal Theory of Social Power,Psych. Review 63 (1956), 181–194.

    Article  MathSciNet  Google Scholar 

  2. [2]

    F. Harary, A Criterion for Unanimity in French’s Theory of Social Power, in:Research, Ann Arbor, Michigan, (1959), 168–182.

    Google Scholar 

  3. [3]

    F. S. Roberts,Discrete Mathematical Models, with Application to Social, Biological, and Environmental Problems, Prentice-Hall, Englewood Cliffs, N. J. 1976.

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

AMS subject classification (1980)

  • 90 A 08