{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "DQ14ERMRTZ"
    },
    {
      "field": "uses",
      "target": "DXWBWMM5H7"
    },
    {
      "field": "uses",
      "target": "HJ1159KYP3"
    },
    {
      "field": "uses",
      "target": "S0DAGR1WN7"
    }
  ],
  "body": "\n## Summary\n\nA majority term is a ternary term $m(x, y, z)$ that returns the value shared by at least two of its three arguments.\nIt is the [[near-unanimity term|4CRH8NNFEF]] of the smallest possible arity.\nLattices and Boolean algebras have a majority term, and every variety with a majority term is congruence-distributive.\nFor a finite algebra with a majority term, the term operations are exactly the operations that preserve the subalgebras of its square.\n\n## Explanations\n\n### L1 human\n\nThree people vote, and the majority term reports the opinion of at least two of them.\nOn the set $\\set{0, 1}$ the majority function is $m(x, y, z) = 1$ exactly when at least two of $x, y, z$ equal $1$.\nFor example $m(1, 0, 1) = 1$ and $m(0, 0, 1) = 0$.\nIn a lattice the same role is played by $(x \\wedge y) \\vee (y \\wedge z) \\vee (x \\wedge z)$, the median of three elements in a chain.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B05",
      "08B10"
    ],
    "name": "Majority term",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Majority_function"
      }
    ],
    "specializes": [
      "4CRH8NNFEF"
    ],
    "tag": "9879ZMW5AA"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/9879ZMW5AA/",
  "links": [
    {
      "field": "specializes",
      "target": "4CRH8NNFEF"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/9879ZMW5AA.md",
  "msc": [
    "08B05",
    "08B10"
  ],
  "name": "Majority term",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/987/9879ZMW5AA.md",
  "status": null,
  "tag": "9879ZMW5AA",
  "uri": "m2://9879ZMW5AA",
  "url": "https://tamnd.github.io/math2/wiki/majority-term/",
  "writing": {
    "tag": "9879ZMW5AA",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}