  Fair ranking problems arise in many decision-making processes that often
necessitate a trade-off between accuracy and fairness. Many existing studies
have proposed correction methods such as adding fairness constraints to a
ranking model's loss. However, the challenge of correcting the data bias for
fair ranking remains, and the trade-off of the ranking models leaves room for
improvement. In this paper, we propose a fair ranking framework that evaluates
the order of training data in a pairwise manner as well as various fairness
measurements in ranking. This study is the first proposal of a pre-processing
method that solves fair ranking problems using the pairwise ordering method
with our best knowledge. The fair pairwise ordering method is prominent in
training the fair ranking models because it ensures that the resulting ranking
likely becomes parity across groups. As far as the fairness measurements in
ranking are represented as a linear constraint of the ranking models, we proved
that the minimization of loss function subject to the constraints is reduced to
the closed solution of the minimization problem augmented by weights to
training data. This closed solution inspires us to present a practical and
stable algorithm that iterates the optimization of weights and model
parameters. The empirical results over real-world datasets demonstrated that
our method outperforms the existing methods in the trade-off between accuracy
and fairness over real-world datasets and various fairness measurements.
