Fairness Auditing in Urban Decisions using LP-based Data Combination

Auditing for fairness often requires relying on a secondary source, e.g., Census data, to inform about protected attributes. To avoid making assumptions about an overarching model that ties such information to the primary data source, a recent line of work has suggested finding the entire range of possible fairness valuations consistent with both sources. Though attractive, the current form of this methodology relies on rigid analytical expressions and lacks the ability to handle continuous decisions, e.g., metrics of urban services. We show that, in such settings, directly adapting these expressions can lead to loose and even vacuous results, particularly on just how fair the audited decisions may be. If used, the audit would be perceived more optimistically than it ought to be. We propose a linear programming formulation to handle continuous decisions, by finding the empirical fairness range when statistical parity is measured through the Kolmogorov-Smirnov distance. The size of this problem is linear in the number of data points and efficiently solvable. We analyze this approach and give finite-sample guarantees to the resulting fairness valuation. We then apply it to synthetic data and to 311 Chicago City Services data, and demonstrate its ability to reveal small but detectable bounds on fairness.