This two-part study provides empirical results for ongoing research and development. The TopDown Algorithm (TDA)  is being planned for use to protect the confidentiality of respondent data collected during the 2020 Census. Following the 2010 Census, swapping was applied to respondent data to protect confidentiality.
In Part I, we propose an empirically based solution to the question: “What is the minimum TOTAL population of a district to have reliable characteristics of various demographic groups". To answer this question, we use data treated by the 2021-04-28 version (ϵ = 10:3, for the person file) of the TDA for all block groups (proxy for districts) in the United States. We also consider “places and minor civil divisions (MCDs)" as proxies for districts. Empirical results suggest minimum TOTAL between 550 and 599 people in a block group provides reliable characteristics of various demographic groups in a block group based on the TDA. A similar minimum TOTAL between 350 and 399 is observed for places and MCDs. No congressional or state legislative district failed our test for reliability.
Part II is an update of our results reported in  where ϵ = 4:0; whereas, throughout this study ϵ = 10:3. The objective here is to assess the variability of data results from application of the 2021-04-28 version TDA to the 2010 Census Edited File (2010 CEF) for Rhode Island and for three additional jurisdictions. Our approach has two parts: (1) to report observations on variability of results among 25 runs of the TDA and (2) to report observations on variability between the results among the 25 runs of the TDA and the published 2010 Census Public Law 94-171 data. We observe that variability in data results from the TDA increases as we consider smaller pieces of geography and population. Most noticeable, variability with the 2021-04-28 version of the TDA (ϵ = 10:3) is less than what we reported in  with the 2019-10-31 version where ϵ = 4:0.