The efficacy of tournament designs

Tournaments are a widely used mechanism to rank alternatives in a noisy environment. We investigate a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the alternatives be compared pairwise to best approximate their true but latent ranking. We consider various formats including knockout tournaments, multi-stage championships consisting of round-robin groups followed by single elimination, and the Swiss-system. They are evaluated via Monte-Carlo simulations under six different assumptions on winning probabilities. Comparing the same pairs of alternatives multiple times turns out to be an inefficacious policy. The Swiss-system is found to be the most accurate among all these designs, especially in its ability to rank all participants. A possible explanation is that it does not eliminate an alternative after a single loss, while it takes the history of the comparisons into account. Hence, this particular format may deserve more attention from the decision-makers such as the governing bodies of major sports.