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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.
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Uncertainty and the Social Planner’s Problem: Why Sample Complexity Matters
Welfare measures overall utility across a population, whereas malfare measures overall disutility, and the social planner’s problem can be cast either as maximizing the former or minimizing the latter. We show novel bounds on the expectations and tail probabilities of estimators of welfare, malfare, and regret of per-group (dis)utility values, where estimates are made from a finite sample drawn from each group. In particular, we consider estimating these quantities for individual functions (e.g., allocations or classifiers) with standard probabilistic bounds, and optimizing and bounding generalization error over hypothesis classes (i.e., we quantify overfitting) using Rademacher averages. We then study algorithmic fairness through the lens of sample complexity, finding that because marginalized or minority groups are often understudied, and fewer data are therefore available, the social planner is more likely to overfit to these groups, thus even models that seem fair in training can be systematically biased against such groups. We argue that this effect can be mitigated by ensuring sufficient sample sizes for each group, and our sample complexity analysis characterizes these sample sizes. Motivated by these conclusions, we present progressive sampling algorithms to efficiently optimize various fairness objectives.
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- Award ID(s):
- 1813444
- PAR ID:
- 10345134
- Date Published:
- Journal Name:
- FAccT '22: 2022 ACM Conference on Fairness, Accountability, and Transparency
- Page Range / eLocation ID:
- 2004 to 2015
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3531146.3533243
