Abstract
In an eight-team single-elimination tournament without reseeding, teams are seeded from best (1) to worst (8). Teams 1/8, 4/5, 2/7 and 3/6 are paired in the first round, with the 1/8 winner facing the 4/5winner in the second round and so on. However, such tournaments are potentially unfair in the sense that inferior teams can be more likely to advance to certain stages of the tournament than better teams. Forinstance, if the top five teams are comparable in strength and are markedly better than the bottom three teams, then seeds 2 and 3 may be more likely to advance to the finals than team 1. We assign each teama unique power value and assume that the victory probability in a match-up is proportional to the teams' powers.We investigate properties of fair tournaments and formulate a non-linear optimization model thatprescribes a fair tournament given the relative strengths of the teams involved. Although the problem is highly non-convex, we demonstrate how to consistently obtain all fair tournaments for 8- and 16-teamproblems.
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