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  "body": "\n## Definition\n\nLet $\\mathcal{V}$ be a [[variety of algebras|AJNZJD8442]].\nA *majority term* for $\\mathcal{V}$ is a ternary [[term|N9M2N27END]] $m(x, y, z)$ such that $\\mathcal{V}$ satisfies the [[identities|PKD440G2XW]]\n$$m(x, x, y) \\approx m(x, y, x) \\approx m(y, x, x) \\approx x.$$\nEquivalently, a majority term is a [[near-unanimity term|4CRH8NNFEF]] of arity $3$.\n\n## Remarks\n\nExample: on $\\set{0, 1}$ the Boolean majority function $m(x, y, z) = (x \\wedge y) \\vee (y \\wedge z) \\vee (x \\wedge z)$ is a majority term of the two-element Boolean algebra.\nCheck: if two arguments equal $a$, then one of the three meets equals $a$ and the other two are at most $a$, so the join is $a$.\nNon-example: the term $p(x, y, z) = x - y + z$ of abelian groups satisfies $p(x, x, y) \\approx y$, not $x$, so it fails the first identity.\nIn fact no variety of groups other than the trivial variety has a majority term, since such a variety is not congruence-distributive.\n",
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