  Tournament organisers supposedly design rules such that a team cannot be
strictly better off by exerting a lower effort. However, the European
qualification tournaments for recent FIFA soccer World Cups are known to
violate this requirement, which inspires our study on the incentive
compatibility of similar group-based qualification systems. Theorems listing
the sufficient and necessary conditions of strategy-proofness are provided and
applied to classify several soccer qualification tournaments for FIFA World
Cups and UEFA European Championships. Two reasonable mechanisms are proposed to
solve the problem of incentive incompatibility: the first is based on
abolishing the anonymity of the matches discarded in the comparison of teams
from different groups, while the second involves a rethinking of the seeding
procedure. Our results have useful implications for the governing bodies of
major sports.
