Discriminative but Not Discriminatory: A Comparison of Fairness Definitions under Different Worldviews

We mathematically compare three competing definitions of group-level nondiscrimination: demographic parity, equalized odds, and calibration. Using the theoretical framework of Friedler et al., we study the properties of each definition under various worldviews, which are assumptions about how, if at all, the observed data is biased. We argue that different worldviews call for different definitions of fairness, and we specify the worldviews that, when combined with the desire to avoid a criterion for discrimination that we call disparity amplification, motivate demographic parity and equalized odds. In addition, we show that calibration is insufficient for avoiding disparity amplification because it allows an arbitrarily large inter-group disparity. Finally, we define a worldview that is more realistic than the previously considered ones, and we introduce a new notion of fairness that corresponds to this worldview.