Geographic Spines in the 2020 Census Disclosure Avoidance System. (arXiv:2203.16654v2 [cs.CR] UPDATED)

The 2020 Census Disclosure Avoidance System (DAS) is a formally private
mechanism that first adds independent noise to cross tabulations for a set of
pre-specified hierarchical geographic units, which is known as the geographic
spine. After post-processing these noisy measurements, DAS outputs a formally
private database with fields indicating location in the standard census
geographic spine, which is defined by the United States as a whole, states,
counties, census tracts, block groups, and census blocks. This paper describes
how the geographic spine used internally within DAS to define the initial noisy
measurements impacts accuracy of the output database. Specifically, tabulations
for geographic areas tend to be most accurate for geographic areas that both 1)
can be derived by aggregating together geographic units above the block
geographic level of the internal spine, and 2) are closer to the geographic
units of the internal spine. After describing the accuracy tradeoffs relevant
to the choice of internal DAS geographic spine, we provide the settings used to
define the 2020 Census production DAS runs.