  Algorithmic fairness has gained prominence due to societal and regulatory
concerns about biases in Machine Learning models. Common group fairness metrics
like Equalized Odds for classification or Demographic Parity for both
classification and regression are widely used and a host of computationally
advantageous post-processing methods have been developed around them. However,
these metrics often limit users from incorporating domain knowledge. Despite
meeting traditional fairness criteria, they can obscure issues related to
intersectional fairness and even replicate unwanted intra-group biases in the
resulting fair solution. To avoid this narrow perspective, we extend the
concept of Demographic Parity to incorporate distributional properties in the
predictions, allowing expert knowledge to be used in the fair solution. We
illustrate the use of this new metric through a practical example of wages, and
develop a parametric method that efficiently addresses practical challenges
like limited training data and constraints on total spending, offering a robust
solution for real-life applications.
