It is often used in sports in order to match teams in knock-out tournaments.
Without further constraints, this problem could easily be solved by finding a random permutation of the winners.
Thus, the goal is to choose a random matching in an incomplete bipartite graph.
At the beginning, there are: The draw proceeds as follows: This procedure yields probabilities that are different than just choosing a matching at random; this creates a distortion in the matching probalities of different groups, which raises suspicion and conspiracy theories.
This draw, too, produces distorted probabilities relative to the uniform-random matching.