  In a generalized tournament, players may have an arbitrary number of matches
against each other and the outcome of the games is measured on a cardinal scale
with a lower and upper bound. An axiomatic approach is applied to the problem
of ranking the competitors. Self-consistency requires assigning the same rank
for players with equivalent results, while a player showing an obviously better
performance than another should be ranked strictly higher. According to order
preservation, if two players have the same pairwise ranking in two tournaments
where the same players have played the same number of matches, then their
pairwise ranking is not allowed to change in the aggregated tournament. We
reveal that these two properties cannot be satisfied simultaneously on this
universal domain.
