The presence of inequity is a fundamental problem in the outcomes of decision-making systems, especially when human lives are at stake. Yet, estimating notions of unfairness or inequity is difficult, particularly if they rely on hard-to-measure concepts such as risk. Such measurements of risk can be accurately obtained when no unobserved confounders have jointly influenced past decisions and outcomes. However, in the real world, this assumption rarely holds. In this paper, we show a surprising result that one can still give meaningful bounds on treatment rates to high-risk individuals, even when entirely eliminating or relaxing the assumption that all relevant risk factors are observed. We use the fact that in many real-world settings (e.g., the release of a new treatment) we have data from prior to any allocation to derive unbiased estimates of risk. This result is of immediate practical interest: we can audit unfair outcomes of existing decision-making systems in a principled manner. For instance, in a real-world study of Paxlovid allocation, our framework provably identifies that observed racial inequity cannot be explained by unobserved confounders of the same strength as important observed covariates.
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