Description

Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices

Similarly to the popular voter model, the Deffuant model describes opinion dynamics taking place in spatially structured environments represented by a connected graph. Pairs of adjacent vertices interact at a constant rate. If the opinion distance between the interacting vertices is larger than some confidence threshold epsilon > 0, then nothing happens, otherwise, the vertices' opinions get closer to each other. It has been conjectured based on numerical simulations that this process exhibits a phase transition at the critical value epsilon(c) = 1/2. For confidence thresholds larger than one half, the process converges to a global consensus, whereas coexistence occurs for confidence thresholds smaller than one half. In this article, we develop new geometrical techniques to prove this conjecture.

Reuse Permissions
  • Downloads
    PDF (285.9 KB)

    Details

    Title
    • The Critical Value of the Deffuant Model Equals One Half
    Contributors
    Date Created
    2012
    Resource Type
  • Text
  • Collections this item is in
    Identifier
    • Identifier Value
      https://math.la.asu.edu/~lanchier/
    • Identifier Type
      International standard serial number
      Identifier Value
      1980-0436
    Note
    • View the article as published at: http://alea.impa.br/english/index_v9.htm

    Citation and reuse

    Cite this item

    This is a suggested citation. Consult the appropriate style guide for specific citation guidelines.

    Lanchier, N. (n.d.). The critical value of the Deffuant model equals one half. ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 9(2), 383–402.

    Machine-readable links