{
  "id": "1205.1075",
  "version": "v1",
  "published": "2012-05-04T21:46:13.000Z",
  "updated": "2012-05-04T21:46:13.000Z",
  "title": "Eulerian Opinion Dynamics with Bounded Confidence and Exogenous Input",
  "authors": [
    "Anahita Mirtabatabaei",
    "Peng Jia",
    "Francesco Bullo"
  ],
  "comment": "6 pages, 2 figures, submitted to IFAC NecSys '12",
  "categories": [
    "math.DS"
  ],
  "abstract": "The formation of opinions in a large population is governed by endogenous (human interactions) and exogenous (media influence) factors. In the analysis of opinion evolution in a large population, decision making rules can be approximated with non-Bayesian \"rule of thumb\" methods. This paper focuses on an Eulerian bounded-confidence model of opinion dynamics with a potential time-varying input. First, we prove some properties of this system's dynamics with time-varying input. Second, we derive a simple sufficient condition for opinion consensus, and prove the convergence of the population's distribution with no input to a sum of Dirac Delta functions. Finally, we define an input's attraction range, and for a normally distributed input and uniformly distributed initial population, we conjecture that the length of attraction range is an increasing affine function of population's confidence bound and input's variance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-04T21:46:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eulerian opinion dynamics",
      "bounded confidence",
      "exogenous input",
      "large population",
      "populations confidence bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1075M"
    }
  }
}