{
  "id": "2102.11768",
  "version": "v1",
  "published": "2021-02-23T16:00:35.000Z",
  "updated": "2021-02-23T16:00:35.000Z",
  "title": "Robust Naive Learning in Social Networks",
  "authors": [
    "Gideon Amir",
    "Itai Arieli",
    "Galit Ashkenazi-Golan",
    "Ron Peretz"
  ],
  "comment": "27 pages",
  "categories": [
    "math.PR",
    "cs.DM",
    "cs.SI",
    "physics.soc-ph"
  ],
  "abstract": "We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from Golub and Jackson that under the DeGroot dynamics agents reach a consensus which is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single `bot' that does not adhere to the updating rule, can sway the public consensus to any other value. We introduce a variant of the DeGroot dynamics which we call \\emph{ $\\varepsilon$-DeGroot}. The $\\varepsilon$-DeGroot dynamics approximates the standard DeGroot dynamics and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to the standard DeGroot dynamics, the $\\varepsilon$-DeGroot dynamics is highly robust both to the presence of bots and to certain types of misspecifications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-23T16:00:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91D30",
      "60C05"
    ],
    "keywords": [
      "social networks",
      "robust naive learning",
      "standard degroot dynamics",
      "degroot dynamics agents reach",
      "degroot dynamics approximates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}