Evolving Fair Linear Regression for the Representation of Human-Drawn Regression Lines

Here we study a generalization of linear regression to the case of maximal elements of a general fairness relation. The regression then is based on balancing the distances to the data points. The studied relations are lexicographic minimum, maxmin fairness, proportional fairness, and majorities, all in a complementary version to represent minimality. A new combination of proportional fairness and majority is introduced as well. Experiments are performed on human subjects solving the visual task to draw a line fitting to given data points, and by use of evolutionary computation (here by Differential Evolution) the weights of a fair linear regression are adjusted to the human-provided results. The fact that this gives a more precise approximation than (weighted) linear regression hints on the inclusion of the balance among the distances to the given data points in the human decision making process.