= Transitive tournament
A <transitive tournament> is a <tournament> whose vertices admit an ordering $v_1,\ldots,v_n$ with every edge directed from $v_i$ to $v_j$ when $i<j$. Equivalently, it has no <directed cycle>, or no directed triangle. The implication from no triangle follows by shortening any shortest directed cycle of length greater than three using its chord.
Its <outdegrees> are $n-1,n-2,\ldots,0$, so the ordering records a consistent ranking with no cyclic preference. Every three-vertex tournament is either transitive or a directed triangle. This makes transitive tournaments the simplest model of a complete pairwise comparison that agrees with a <total order>.
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