{
  "id": "cond-mat/0408648",
  "version": "v1",
  "published": "2004-08-30T11:50:19.000Z",
  "updated": "2004-08-30T11:50:19.000Z",
  "title": "On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann",
  "authors": [
    "Santo Fortunato"
  ],
  "comment": "15 pages, 7 figures, to appear in International Journal of Modern Physics C 16, issue 2 (2005)",
  "doi": "10.1142/S0129183105007078",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \\epsilon. A randomly chosen agent takes the average of the opinions of all neighbouring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold \\epsilon_c of this model. We claim that \\epsilon_c can take only two possible values, depending on the behaviour of the average degree d of the graph representing the social relationships, when the population N goes to infinity: if d diverges when N goes to infinity, \\epsilon_c equals the consensus threshold \\epsilon_i ~ 0.2 on the complete graph; if instead d stays finite when N goes to infinity, \\epsilon_c=1/2 as for the model of Deffuant et al.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-30T11:50:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consensus threshold",
      "opinion dynamics",
      "krause-hegselmann",
      "confidence bound parameter",
      "complete graph"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}