A note on the multiplicative fairness score in the NIJ recidivism forecasting challenge

Abstract

Background: The 2021 NIJ recidivism forecasting challenge asks participants to construct predictive models of recidivism while balancing false positive rates across groups of Black and white individuals through a multiplicative fairness score. We investigate the performance of several models for forecasting 1-year recidivism and optimizing the NIJ multiplicative fairness metric. Methods: We consider standard linear and logistic regression, a penalized regression that optimizes a convex surrogate loss (that we show has an analytical solution), two post-processing techniques, linear regression with re-balanced data, a black-box general purpose optimizer applied directly to the NIJ metric and a gradient boosting machine learning approach. Results: For the set of models investigated, we find that a simple heuristic of truncating scores at the decision threshold (thus predicting no recidivism across the data) yields as good or better NIJ fairness scores on held out data compared to other, more sophisticated approaches. We also find that when the cutoff is further away from the base rate of recidivism, as is the case in the competition where the base rate is 0.29 and the cutoff is 0.5, then simply optimizing the mean square error gives nearly optimal NIJ fairness metric solutions. Conclusions: The multiplicative metric in the 2021 NIJ recidivism forecasting competition encourages solutions that simply optimize MSE and/or use truncation, therefore yielding trivial solutions that forecast no one will recidivate.