Why qualifications at the Olympics?

Abstract

"The optimal contest architecture for symmetric imperfectly discriminating contests isnshown to be generically the two-stage tournament (rather than the one-stage contest). In the first stage the contestants compete in several parallel divisions for the right to participate in the secondnstage. In the second stage the short-listed finalists compete for the prize. Given a sufficient number of contestants, the two-stage tournament is either strictly better or at least as good as the one-stage contest for maximizing an individual’s effort, for maximizing the aggregate effort andnfor minimizing the standard deviation of effort. For maximizing an individual’s effort it is generally optimal to have only two finalists in the second stage. For maximizing the aggregate effort or minimizing the standard deviation of effort the optimal number of finalists in the second stage depends on the discriminating power of the contest success function."