Assessing the fairness of a decision making system with respect to a protected class, such as gender or race, is challenging when class membership labels are unavailable. Probabilistic models for predicting the protected class based on observable proxies, such as surname and geolocation for race, are sometimes used to impute these missing labels for compliance assessments. Empirically, these methods are observed to exaggerate disparities, but the reason why is unknown. In this paper, we decompose the biases in estimating outcome disparity via threshold-based imputation into multiple interpretable bias sources, allowing us to explain when over- or underestimation occurs. We also propose an alternative weighted estimator that uses soft classification, and show that its bias arises simply from the conditional covariance of the outcome with the true class membership. Finally, we illustrate our results with numerical simulations and a public dataset of mortgage applications, using geolocation as a proxy for race. We confirm that the bias of threshold-based imputation is generally upward, but its magnitude varies strongly with the threshold chosen. Our new weighted estimator tends to have a negative bias that is much simpler to analyze and reason about.
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Assessing Algorithmic Fairness with Unobserved Protected Class Using Data Combination
The increasing impact of algorithmic decisions on people’s lives compels us to scrutinize their fairness and, in particular, the disparate impacts that ostensibly color-blind algorithms can have on different groups. Examples include credit decisioning, hiring, advertising, criminal justice, personalized medicine, and targeted policy making, where in some cases legislative or regulatory frameworks for fairness exist and define specific protected classes. In this paper we study a fundamental challenge to assessing disparate impacts in practice: protected class membership is often not observed in the data. This is particularly a problem in lending and healthcare. We consider the use of an auxiliary data set, such as the U.S. census, to construct models that predict the protected class from proxy variables, such as surname and geolocation. We show that even with such data, a variety of common disparity measures are generally unidentifiable, providing a new perspective on the documented biases of popular proxy-based methods. We provide exact characterizations of the tightest possible set of all possible true disparities that are consistent with the data (and possibly additional assumptions). We further provide optimization-based algorithms for computing and visualizing these sets and statistical tools to assess sampling uncertainty. Together, these enable reliable and robust assessments of disparities—an important tool when disparity assessment can have far-reaching policy implications. We demonstrate this in two case studies with real data: mortgage lending and personalized medicine dosing. This paper was accepted by Hamid Nazerzadeh, Guest Editor for the Special Issue on Data-Driven Prescriptive Analytics.
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- Award ID(s):
- 1939704
- NSF-PAR ID:
- 10227065
- Date Published:
- Journal Name:
- Management Science
- ISSN:
- 0025-1909
- 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
- Journal Article:
- https://doi.org/10.1287/mnsc.2020.3850
