  The quantification of modern slavery has received increased attention
recently as organizations have come together to produce global estimates, where
multiple systems estimation (MSE) is often used to this end. Echoing a
long-standing controversy, disagreements have re-surfaced regarding the
underlying MSE assumptions, the robustness of MSE methodology, and the accuracy
of MSE estimates in this application. Our goal is to help address and move past
these controversies. To do so, we review MSE, its assumptions, and commonly
used models for modern slavery applications. We introduce all of the publicly
available modern slavery datasets in the literature, providing a reproducible
analysis and highlighting current issues. Specifically, we utilize an internal
consistency approach that constructs subsets of data for which ground truth is
available, allowing us to evaluate the accuracy of MSE estimators. Next, we
propose a characterization of the large sample bias of estimators as a function
of misspecified assumptions. Then, we propose an alternative to traditional
(e.g., bootstrap-based) assessments of reliability, which allows us to
visualize trajectories of MSE estimates to illustrate the robustness of
estimates. Finally, our complementary analyses are used to provide guidance
regarding the application and reliability of MSE methodology.
