Stronger players win more knockout tournaments in average
A knockout tournament plan for n players can be considered as a rooted binary tree with n terminal nodes which serve as the starting positions for the players. A labeling means an assignment of the players each to a distinct terminal node. Associated with the set of players is a preference scheme which specifies for all possible pairs the probability of one player beating another in a game.It has been conjectured that if the preference scheme satisfies strong stochastic transitivity, then stronger players (as defined by the preference scheme) should have larger prob¬abilities to win a tournament for any given tournament plan, assuming each labeling is equally likely. In this article, we give some insight into the difficulties in proving the conjecture. As evidence for the conjecture's validity, we show that if we give some insight into the difficulties in proving the conjecture . As evidence for the conjectures validity,we show that if we average over all tournament plans, assuming each plan is equally li...