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Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may therefore fail to achieve the kind of fairness that is desired for disadvantaged groups. In addition, they are often incompatible with each other, and there is no convincing justification for selecting one rather than another. This paper explores whether a broader conception of social justice, based on optimizing a social welfare function (SWF), can be useful for assessing various definitions of parity. We focus on the well-known alpha fairness SWF, which has been defended by axiomatic and bargaining arguments over a period of 70 years. We analyze the optimal solution and show that it can justify demographic parity or equalized odds under certain conditions, but frequently requires a departure from these types of parity. In addition, we find that predictive rate parity is of limited usefulness. These results suggest that optimization theory can shed light on the intensely discussed question of how to achieve group fairness in AI. 

We consider a setting in which a social planner has to make a sequence of decisions to allocate scarce resources in a high-stakes domain. Our goal is to understand stakeholders' dynamic moral preferences toward such allocational policies. In particular, we evaluate the sensitivity of moral preferences to the history of allocations and their perceived future impact on various socially salient groups. We propose a mathematical model to capture and infer such dynamic moral preferences. We illustrate our model through small-scale human-subject experiments focused on the allocation of scarce medical resource distributions during a hypothetical viral epidemic. We observe that participants' preferences are indeed history- and impact-dependent. Additionally, our preliminary experimental results reveal intriguing patterns specific to medical resources---a topic that is particularly salient against the backdrop of the global covid-19 pandemic.