Popularity Preserving Fair Matching

This paper discusses on the fairness on the context of two-sided matching. This paper proposes a new definition of individual fairness for two-sided matching, called Popularity Preserving Fairness (PPF). It is the first definition of individual fairness for two-sided matching that does not have to make the model more complex. The new definition of PPF means that the wish of a person with higher popularity takes priority over that of a lower person. This paper also proposes a relaxed version of PPF with thresholds
$k, \ell$
because a PPF matching does not always exist. The relaxed definition allows a person
$B$
whose popular rank is below that of
$A$
within
$k$
to match a person whose rank in
$B$
's preference order is lower than that of
$A$
and lor regards the difference of ranks of matched people is within
$\ell$
as a not different case. Furthermore, this paper provides an efficient decision algorithm for PPF matching.