Fair Seeding in Knockout Tournaments
We investigated the existence of fair seeding in knockout tournaments. We define two fairness criteria, both adapted from the literature: envy-freeness and order preservation. We show how to achieve the first criterion in tournaments whose structure is unconstrained, and prove an impossibility result for balanced tournaments. For the second criterion we have a similar result for unconstrained tournaments, but not for the balanced case. We provide instead a heuristic algorithm which we show through experiments to be efficient and effective. This suggests that the criterion is achievable also in balanced tournaments. However, we prove that it again becomes impossible to achieve when we add a weak condition guarding against the phenomenon of tournament dropout.
knockout tournament heuristic algorithm design