There is a lack of consensus within the literature as to how `fairness' of algorithmic systems can be measured, and different metrics can often be at odds. In this paper, we approach this task by drawing on the ethical frameworks of utilitarianism and John Rawls. Informally, these two theories of distributive justice measure the `good' as either a population's sum of utility, or worst-off outcomes, respectively. We present a parameterized class of objective functions that interpolates between these two (possibly) conflicting notions of the `good'. This class is shown to represent a relaxation of the Rawlsian `veil of ignorance', and its sequence of optimal solutions converges to both a utilitarian and Rawlsian optimum. Several other properties of this class are studied, including: 1) a relationship to regularized optimization, 2) feasibility of consistent estimation, and 3) algorithmic cost. In several real-world datasets, we compute optimal solutions and construct the tradeoff between utilitarian and Rawlsian notions of the `good'. Empirically, we demonstrate that increasing model complexity can manifest strict improvements to both measures of the `good'. This work suggests that the proper degree of `fairness' can be informed by a designer's preferences over the space of induced utilitarian and Rawlsian `good'.

翻译：文献界对于如何衡量算法系统的“公平性”缺乏共识，且不同指标往往相互矛盾。本文借鉴功利主义与约翰·罗尔斯的伦理框架来处理这一问题。非正式而言，这两种分配正义理论分别将“福祉”衡量为群体效用总和或最差个体的结果。我们提出了一类参数化的目标函数，可在这两种（可能冲突的）“福祉”概念之间进行插值。研究表明，此类函数代表了对罗尔斯“无知之幕”的松弛，其最优解序列收敛于功利主义与罗尔斯主义的双重最优解。我们还研究了该函数类的其他若干性质，包括：1）与正则化优化的关系，2）一致估计的可行性，3）算法代价。在多个真实数据集中，我们计算了最优解并构建了功利主义与罗尔斯主义“福祉”概念之间的权衡曲线。实验表明，增加模型复杂度可同时显著提升两种“福祉”指标。本研究表明，设计者对功利主义与罗尔斯主义“福祉”空间中的偏好可指导“公平性”的恰当程度。