A Rawlsian Mixed Integer Programming Approach for Fair Classification

William Yang, Ryan Feng Lin, Chaoyue Zhao, Shuai Huang

Abstract: Binary classification is a common machine learning methodology that aims to partition data into two classes as accurately as possible. One major drawback of these methods is that they are prone to producing unfair results. One real-life example of this is the Correctional Offender Management Profiling for Alternative Sanctions algorithm, which was designed to label individuals as "low" or "high" risk for recidivism. The algorithm produced predictions that had significantly worse accuracy for individuals in one demographic group than in others. While many methods have been proposed to address this, they are known to sacrifice overall prediction accuracy for the whole population. We present a Rawlsian fairness approach that prioritizes algorithmic performance for the worst-off demographic group without sacrificing overall performance. We couple our Rawlsian fairness approach with a scoring system using a mixed integer programming (MIP) formulation. Our approach assigns a score to each individual and assigns them to a class if it is above or below a specific threshold. By using an MIP approach, we can solve for the optimal threshold rather than relying on the user to identify the threshold before executing the method. Our MIP approach is also flexible, as it provides the user with multiple ways to obtain sparse or integer solutions. Our results yield fair outcomes even when a particular group comprises a small proportion of the entire dataset and provide insight into how our methodology compares to other fairness approaches.