The alleged threat of reconstruction attacks has led the U.S. Census Bureau (USCB) to replace in the Decennial Census 2020 the traditional statistical disclosure limitation based on rank swapping with one based on differential privacy (DP). This has resulted in substantial accuracy loss of the released statistics. Worse yet, it has been shown that the reconstruction attacks used as an argument to move to DP are very far from allowing unequivocal reidentification of the respondents, because in general there are a lot of reconstructions compatible with the released statistics. In a very recent paper, a new reconstruction attack has been proposed, whose goal is to indicate the confidence that a reconstructed record was in the original respondent data. The alleged risk of serious disclosure entailed by such confidence-ranked reconstruction has renewed the interest of the USCB to use DP-based solutions. To forestall the potential accuracy loss in future data releases resulting from adoption of these solutions, we show in this paper that the proposed confidence-ranked reconstruction does not threaten privacy. Specifically, we report empirical results showing that the proposed ranking cannot guide reidentification or attribute disclosure attacks, and hence it fails to warrant the USCB's move towards DP. Further, we also demonstrate that, due to the way the Census data are compiled, processed and released, it is not possible to reconstruct original and complete records through any methodology, and the confidence-ranked reconstruction not only is completely ineffective at accurately reconstructing Census records but is trivially outperformed by an adequate interpretation of the released aggregate statistics.

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.