  Recently, many matching systems around the world have been reformed. These
reforms responded to objections that the matching mechanisms in use were unfair
and manipulable. Surprisingly, the mechanisms remained unfair even after the
reforms: the new mechanisms may induce an outcome with a blocking student who
desires and deserves a school which she did not receive. However, as we show in
this paper, the reforms introduced matching mechanisms which are more fair
compared to the counterfactuals. First, most of the reforms introduced
mechanisms that are more fair by stability: whenever the old mechanism does not
have a blocking student, the new mechanism does not have a blocking student
either. Second, some reforms introduced mechanisms that are more fair by
counting: the old mechanism always has at least as many blocking students as
the new mechanism. These findings give a novel rationale to the reforms and
complement the recent literature showing that the same reforms have introduced
less manipulable matching mechanisms. We further show that the fairness and
manipulability of the mechanisms are strongly logically related.
