Some Monotone Almost Balanced Knockout Tournament Plans

Knockout tournaments are often used in sports (or experiments where- preferences are registered by comparisons instead of measurements) to determine the champion of an event. A knockout tournament plan (KTP) for n players is a rooted binary tree with n leaves to be labelled by the n players. Each subtree of two leaves represents a match between the two players labelling the two leaves, the winner of the match then moves on to label the root of the subtree. While there are many KTPs to choose from for a given number of players, in the real world an almost balanced KTP is usually chosen. One reason could be the perception that a balanced KTP is "fair" to the players in the sense that, given a random labelling of leaves by players, a stronger player has a better chance to win the tournament.