Abstract
Suppose that in a three-player tournament the strongest player, A 1, meets the winner of the match between A 2 and the weakest player, A 3. It is shown that, for A 1 and A 2 of fixed strength, A 1's chances of winning may be increased if A 3 is replaced by a stronger player. The paradox is studied with special emphasis on probability models important in the method of paired comparisons.
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