 Comparison tournament

Pair candidates from a totally ordered set and retain the greater one from each comparison until one winner remains. Every other candidate loses once, so $n-1$ key comparisons suffice to find the maximum of $n$ distinct values. A balanced tournament on $2^m$ inputs gives the winner $m$ direct losers. Retaining each loser's own defeat record preserves information for finding later order statistics. The comparison records form a rooted tree and are distinct from a graph-theoretic tournament, which includes a directed comparison between every pair.