The Predictive Power of Noisy Elimination Tournaments

An elimination tournament matches players pairwise and promotes the winners to a subsequent round where the procedure is repeated. In the presence of idiosyncratic noise the tournament turns into a probabilistic mechanism that reveals the ranking of players imperfectly. I assess theoretically the power of such a mechanism to determine the ex ante best player as the winner, as a function of the number of players, their distribution of type, and the noise level. I consider also various seeding strategies and show that for large and small noise (as compared to the variance of ability distribution among players), seeding and other control parameters of tournament design tend to play no role, whereas for intermediate noise level the predictive power depends strongly on the control parameters and therefore can be systematically manipulated by the principal.