  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.
