{
  "id": "1407.7763",
  "version": "v2",
  "published": "2014-07-29T16:05:14.000Z",
  "updated": "2014-08-04T19:47:43.000Z",
  "title": "Social choice, computational complexity, Gaussian geometry, and Boolean functions",
  "authors": [
    "Ryan O'Donnell"
  ],
  "comment": "In proceedings of the 2014 ICM. Corrected a few minor typos from previous version",
  "categories": [
    "math.PR",
    "cs.CC",
    "cs.DM"
  ],
  "abstract": "We describe a web of connections between the following topics: the mathematical theory of voting and social choice; the computational complexity of the Maximum Cut problem; the Gaussian Isoperimetric Inequality and Borell's generalization thereof; the Hypercontractive Inequality of Bonami; and, the analysis of Boolean functions. A major theme is the technique of reducing inequalities about Gaussian functions to inequalities about Boolean functions f : {-1,1}^n -> {-1,1}, and then using induction on n to further reduce to inequalities about functions f : {-1,1} -> {-1,1}. We especially highlight De, Mossel, and Neeman's recent use of this technique to prove the Majority Is Stablest Theorem and Borell's Isoperimetric Inequality simultaneously.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-04T19:47:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91B14",
      "03D15",
      "94C10",
      "51M16",
      "60G15",
      "G.1.6",
      "F.2.2"
    ],
    "keywords": [
      "boolean functions",
      "computational complexity",
      "social choice",
      "gaussian geometry",
      "maximum cut problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7763O"
    }
  }
}