The selection efficiency of tournaments

We discuss tournaments in terms of their efficiency as probabilistic mechanisms that select high-quality alternatives ("players") in a noisy environment. We characterize the selection efficiency of three such mechanisms - contests, binary elimination tournaments, and round-robin tournaments - depending on the shape of the distribution of players' quality, the number of players, and noise level. The results have implications as to how, and under what circumstances, the efficiency of tournament-based selection can be manipulated.