  In this paper, we propose an experimental investigation of the problem of AI
fairness in classification. We train an AI model and develop our own fairness
package FairDream to detect inequalities and then to correct for them, using
income prediction as a case study. Our experiments show that it is a property
of FairDream to fulfill fairness objectives which are conditional on the ground
truth (Equalized Odds), even when the algorithm is set the task of equalizing
positives across groups (Demographic Parity). While this may be seen as an
anomaly, we explain this property by comparing our approach with a closely
related fairness method (GridSearch), which can enforce Demographic Parity at
the expense of Equalized Odds. We grant that a fairness metric conditioned on
true labels does not give a sufficient criterion to reach fairness, but we
argue that it gives us at least a necessary condition to implement Demographic
Parity cautiously. We also explain why neither Equal Calibration nor Equal
Precision stand as relevant fairness criteria in classification. Addressing
their limitations to warn the decision-maker for any disadvantaging rate,
Equalized Odds avoids the peril of strict conservatism, while keeping away the
utopia of a whole redistribution of resources through algorithms.
