Table 1.

Performance of constrained and penalized regression methods

		Predictive ratio		Net compensation
Method	R 2	g	$g^c$	g	$g^c$	Mean residual difference	Fair covariance
Average	12.4%	0.996	1.001	−$46	$4	−$50	6
Covariance	12.4	0.996	1.001	−46	4	−50	6
Net compensation*	12.5	0.980	1.006	−232	34	−266	31
Weighted average†	12.6	0.964	1.011	−411	62	−473	56
Mean residual difference‡	12.8	0.895	1.032	−1208	188	−1396	164
OLS	12.9	0.837	1.050	−1872	293	−2165	256

^* $\lambda =10000$.

^† $\alpha =0.2$.

^‡ $\lambda =30000$.

Note: Measures calculated based on cross‐validated predicted values and sorted on net compensation. Best performing hyperparameters for each estimator (with respect to fairness measures) are displayed. Performance for covariance method was same for all m. $g^c$ is the complement of g.