Opinion Formation and Phase Transitions in a Probabilistic Cellular Automaton with Two Absorbing States

  • Franco Bagnoli
  • Fabio Franci
  • Raúl Rechtman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2493)

Abstract

We discuss the process of opinion formation in a completely homogeneous, democratic population using a class of probabilistic cellular automata models with two absorbing states. Each individual can have one of two opinions that can change according to that of his neighbors. It is dominated by an overwhelming majority and can disagree against a marginal one. We present the phase diagram in the mean field approximation and from numerical experiments for the simplest nontrivial case. For arbitrarily large neighborhoods we discuss the mean field results for a non-conformist society, where each individual adheres to the overwhelming majority of its neighbors and choses an opposite opinion in other cases. Mean field results and preliminary lattice simulations with long-range connections among individuals show the presence of coherent temporal oscillations of the population.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Latané, B.: American Psychologist 36 (1981) 343CrossRefGoogle Scholar
  2. 2.
    Galam, S., Gefen, Y., Shapir, Y.: Math. J. of Sociology 9, (1982) 1MATHCrossRefGoogle Scholar
  3. 3.
    Holyst, J.A., Kacperski, K, Schweitzer, F.: Physica A 285 (2000) 199MATHCrossRefGoogle Scholar
  4. 4.
    Galam, S., Chopard, B., Masselot, A., Droz, M.: Eur. Phys. J. B 4, (1998) 529Google Scholar
  5. 5.
    Chopard, B., Droz, M., Galam, S.: Eur. Phys. J. B 16, (2000) 575Google Scholar
  6. 6.
    Bagnoli, F., Boccara, N., Rechtman, R.: Phys. Rev. E 63 (2001) 46116; condmat /0002361CrossRefGoogle Scholar
  7. 7.
    Watts, D. J., Strogatz S. H.: Nature 393 (1998) 440CrossRefGoogle Scholar
  8. 8.
    Vichniac, G. Y.: Cellular Automata Models of Disorder and Organization In Bienestok, E., Fogelman, F., Weisbuch, G. (eds.), Disordered Systems and Biological Organization, NATO ASI Series, b F20/b, Berlin: Springer Verlag (1986) pp. 283–293; http://www.fourmilab.ch/cellab/manual/cellab.html Google Scholar
  9. 9.
    Wolfram, S.: Rev. Mod. Phys. 55 (1983) 601CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Bagnoli, F., Rechtman, R., Ruffo, S.: Phys. Lett. A 172 (1992) 34 (1992).CrossRefGoogle Scholar
  11. 11.
    Grassberger, P., von der Twer, T.: J. Phys. A: Math. Gen. 17 (1984) L105; Grassberger, P.: J. Phys. A: Math. Gen. 22 (1989) L1103CrossRefGoogle Scholar
  12. 12.
    Hinrichsen, H. Phys. Rev. E 55 (1997) 219CrossRefGoogle Scholar
  13. 13.
    Kinzel, W. In Deutsch, G., Zallen, R., Adler, J. (eds.): Percolation Structures and Processes, Adam Hilger, Bristol (1983); Kinzel, E., Domany, W.: Phys. Rev. Lett. 53 (1984) 311; Grassberger, P.: J. Stat. Phys. 79 (1985) 13Google Scholar
  14. 14.
    Hinrichsen, H., Weitz, J.S., Domany, E.: J. Stat. Phys. 88 (1997) 617MATHCrossRefGoogle Scholar
  15. 15.
    Muñoz, M.A., Dickman, R., Vespignani, A., Zapperi, S.: Phys. Rev. E 59 (1999) 6175CrossRefGoogle Scholar
  16. 16.
    Jensen, I.: Phys. Rev. E 50 (1994) 3263CrossRefGoogle Scholar
  17. 17.
    Jensen, I., Dickman, R., Phys. Rev. E 48 (1993) 1710CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Franco Bagnoli
    • 1
    • 4
  • Fabio Franci
    • 2
    • 4
  • Raúl Rechtman
    • 3
  1. 1.Dipartimento di EnergeticaUniversità di FirenzeFirenzeItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly
  3. 3.Centro de Investigacíon en EnergíaUNAMTemixco, MorelosMexico
  4. 4.INFMSezione di FirenzeItaly

Personalised recommendations