We mathematically compare four competing definitions of group-level nondiscrimination: demographic parity, equalized odds, predictive parity, 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. We also argue that predictive parity and calibration are insufficient for avoiding disparity amplification because predictive parity allows an arbitrarily large inter-group disparity and calibration is not robust to post-processing. 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.

翻译：我们从数学上比较了群体一级不歧视的四个相互竞争的定义:人口均等、均等概率、预测性均等和校准。我们利用弗里德勒等人的理论框架,研究不同世界观中每个定义的属性,这些定义的假设涉及观察的数据如何,如果有偏差的话。我们争辩说,不同的世界观要求不同的公平定义,我们具体说明了世界观,当我们想要避免一种我们称之为差异扩大、激励人口均等和均等率的歧视标准时,我们又明确指出,预测性均等和校准不足以避免差异扩大,因为预测性均等允许任意的较大群体间差异,而校准对于后处理来说并不有力。最后,我们定义了一个比以往所考虑的世界观更现实的世界观,我们提出了与这一世界观相对应的新的公平观。