We study knockout tournaments using a set of players with which a (pairwise) preference scheme is associated. We show that if the preference scheme is of the Bradley-Terry type, then for any knockout tournament, if player i has a larger merit value than player j, he also has a greater probability of winning the tournament. When the preference scheme is not of the Bradley-Terry type, counterexamples are given for several of the main results.
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Chung et al. (1978) studied this question.
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