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The Impact of the U.S. Census Disclosure Avoidance System on Redistricting and Voting Rights Analysis

Christopher T. Kenny, Shiro Kuriwaki, Cory McCartan, Evan Rosenman, Tyler Simko, Kosuke Imai

arXiv:2105.14197v3stat.APcs.CY

TL;DR

The paper asks how Census privacy protections affect redistricting and voting-rights analysis. It evaluates DAS-protected 2010 Census data with simulation and analytical methods, finding systematic errors across population, partisan, and racial analyses. The authors conclude that these errors can impair redistricting practice, while the finalized 2020 DAS remained unevaluated.

  • Problem

    The paper examines how adding privacy-protecting noise to Census data affects redistricting and voting-rights analyses that rely on those data.

    Source: §1 · p. 3, §7 · p. 17

  • Method

    The authors analyze 2010 Census DAS demonstration data using redistricting simulations and voting-rights analyses, treating the protected data as-is.

    Source: §1 · p. 3, §4 · p. 11, §7 · p. 17

  • Results

    DAS noise shifts population from racially heterogeneous and mixed-partisanship areas, creates unpredictable district-level biases, and makes meeting current One Person, One Vote standards difficult or effectively impossible in some cases.

    Source: §8 · p. 21

  • Takeaways & Limitations

    Privacy protection can decrease Census accuracy, and the authors argue its burdens should not fall disproportionately on people of particular races or political preferences.

    Source: §8 · p. 22

    The finalized DAS could not be evaluated because updated demonstration data were not yet available, and its asymmetric, deterministic post-processing makes statistical adjustment difficult for common models.

    Source: §1 · p. 4, §8 · p. 21

Abstract

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The US Census Bureau plans to protect the privacy of 2020 Census respondents through its Disclosure Avoidance System (DAS), which attempts to achieve differential privacy guarantees by adding noise to the Census microdata. By applying redistricting simulation and analysis methods to DAS-protected 2010 Census data, we find that the protected data are not of sufficient quality for redistricting purposes. We demonstrate that the injected noise makes it impossible for states to accurately comply with the One Person, One Vote principle. Our analysis finds that the DAS-protected data are biased against certain areas, depending on voter turnout and partisan and racial composition, and that these biases lead to large and unpredictable errors in the analysis of partisan and racial gerrymanders. Finally, we show that the DAS algorithm does not universally protect respondent privacy. Based on the names and addresses of registered voters, we are able to predict their race as accurately using the DAS-protected data as when using the 2010 Census data. Despite this, the DAS-protected data can still inaccurately estimate the number of majority-minority districts. We conclude with recommendations for how the Census Bureau should proceed with privacy protection for the 2020 Census.

1 Introduction

The paper evaluates how noise in the Census Bureau’s Disclosure Avoidance System affects redistricting and voting-rights analysis, using redistricting simulations and the 2010 Census demonstration data. It finds systematic racial and partisan biases, risks to population parity, and consequential changes in individual race predictions, while noting that the final 2020 DAS could not yet be evaluated.

1 Introduction

  • The evaluation uses the final pre-release 2010 Census Demonstration Data and assumes practitioners use DAS-protected data as-is, without accounting for the noise-generation mechanism.The authors use recently developed simulation methods to generate realistic maps under legal and other constraints, including contiguity, compactness, and population parity.Source: §1 · p. 3
  • DAS noise transfers population across geographies in ways that reduce racial and partisan heterogeneity, sometimes changing majority-minority district counts and making equal-population compliance difficult.Actual population deviations can be several times larger than DAS-reported deviations, with a greater problem in smaller districts.Source: §1 · p. 3
  • Overall BISG race-prediction accuracy does not decline with DAS data, but individual predictions can shift, underpredicting minority voters and producing fewer majority-minority districts in East Ramapo.BISG combines Census block-level racial proportions with voter names and addresses.Source: §1 · pp. 3–4
  • The finalized 2020 DAS could not be evaluated because updated demonstration data would not be available until weeks after the Census data release.The Bureau planned to increase the privacy-loss budget and modify post-processing; the authors caution that unresolved flaws may affect redistricting.Source: §1 · p. 4
  • The study extends earlier work using an older DAS version by examining redistricting across multiple states, levels, and use cases.The authors describe their study as the broadest look at the impact of the new DAS methodologies on redistricting use to date.Source: §1 · p. 4

2 Overview of Simulation Analysis

The paper compares original Census counts with two DAS-protected versions across redistricting settings, then describes how it evaluates population parity, partisan effects, racial effects, and voting-rights analysis.

2 Overview of Simulation Analysis

  • The analysis compares Census 2010 with DAS-12.2 and DAS-4.5 data across federal, state, and local settings, using redistricting samplers to generate realistic plans under population-parity constraints.DAS-12.2 has a roughly 1.0% precinct-count difference from Census, versus about 1.9% for DAS-4.5; the study examines how precinct-level differences propagate into district-level noise.Source: §2 · pp. 4–5

2.1 Population Parity

  • Population-parity analysis simulates Pennsylvania congressional and Louisiana State Senate maps using DAS data, then checks their deviations against 2010 Census populations.The study measures the maximum percent deviation from average district population and compares it with population-parity standards.Source: §2.1 · pp. 5–6

2.2 Partisan Effects

  • The partisan analysis compares simulated plans from four states across the three data sources and examines precinct-level population-error patterns; close elections motivate the inquiry.The passage notes 25 U.S. House races decided by less than one percentage point in 2012–2020 and 228 state legislative races in 2012–2016.Source: §2.2 · pp. 6–7

2.3 Racial Effects

  • The racial analysis examines whether DAS counts vary systematically across racial groups and whether DAS-based mapmaking changes majority-minority district outcomes.It focuses on the Bureau’s choice to target accuracy to the majority racial group in an area.Source: §2.3 · p. 7

2.4 Ecological Inference and Voting Rights Analysis

  • For voting-rights analysis, the authors assess BISG accuracy where voter-file race is recorded, then reanalyze the East Ramapo school-board case using DAS data.BISG imputes voter race and ethnicity from Census data and surnames; the case analysis compares DAS-based results with those based on the 2010 Census.Source: §2.4 · p. 7

3 Racial and Partisan Undercounting Biases

The section finds that DAS-protected population errors vary with precinct racial composition, partisanship, and turnout. Racially heterogeneous and moderately Democratic precincts tend to lose population, while higher-turnout precincts tend to gain it.

3 Racial and Partisan Undercounting Biases

  • DAS post-processing enforces nonnegative, consistent counts and can introduce area-level bias; a GAM of precinct characteristics explains 9–12% of population-error variance.The model uses Democratic vote share, turnout, density, white population share, and racial heterogeneity.Source: §3 · pp. 7–8
  • Mixed White/nonwhite precincts lose the most population relative to more homogeneous precincts, with fitted error declining as racial diversity rises.Figures 1 and 2 show the model-smoothed error patterns by minority share and racial heterogeneity.Source: §3 · pp. 8–9, Figure 1 · p. 8, Figure 2 · p. 9
  • DAS targets prioritize the largest racial group, which may undercount heterogeneous areas where population differences between racial groups are relatively small.The authors say accuracy guarantees are lower in highly heterogeneous precincts, and that population movement toward homogeneous precincts would tend to increase apparent racial segregation.Source: §3 · p. 9
  • Moderately Democratic precincts are assigned less population, while higher-turnout precincts are assigned more; average effects are 5–15 voters per precinct.The same pattern appeared in DAS-4.5 data with roughly double the fitted-error magnitude.Source: §3 · p. 9, Figure 3 · p. 10
  • DAS-12.2 population changes averaged 308 people across 70 congressional districts, but averaged 2,151 people in two Pennsylvania districts in and around Philadelphia.The measured difference under DAS was orders of magnitude larger than the difference under 2010 block population numbers.Source: §3 · p. 10
  • The authors cannot identify the exact origins of partisan and racial biases without more detail on DAS post-processing and parameters.They nevertheless describe differential population bias by partisanship, turnout, and racial diversity as concerning.Source: §3 · p. 10

4 Population Parity in Redistricting

DAS noise makes commonly used population-parity thresholds unreliable: plans that meet a constraint in one dataset can exceed it when evaluated with another. The mismatch is especially acute for smaller legislative districts.

4 Population Parity in Redistricting

  • DAS noise prevents commonly used population-deviation thresholds from reliably producing equal-population maps, with larger and less predictable deviations in smaller legislative districts.Because practitioners will have only one dataset in practice, they cannot clearly improve estimates of the actual deviation.Source: §4 · p. 11

4.1 Congressional Districts in Pennsylvania

  • 9,915 of 10,000 DAS-12.2 Pennsylvania maps exceeded the 0.1% population-deviation threshold when evaluated using 2010 Census data.Plans drawn to meet the threshold in one dataset had much larger deviations when measured against another.Source: §4.1 · p. 11, Figure 4 · p. 11

4.2 State Legislative Districts in Louisiana

  • At tolerances as generous as 1.0%, all generated Louisiana State Senate plans were invalid in some cases; cross-dataset invalidity increased as tolerances tightened.DAS noise was relatively larger at smaller scales than in Pennsylvania congressional districts.Source: §4.2 · p. 12, Figure 5 · p. 12

5 Partisan Effects on Redistricting

The authors compare enacted plans with simulated partisan outcomes to assess how DAS data affect packing and cracking analyses. Across simulated plans, partisan outcome distributions differ unpredictably across data sources.

5 Partisan Effects on Redistricting

  • The analysis compares enacted-plan votes with simulated-plan distributions, whose district-level patterns may depend on whether diverse precincts are spatially clustered.A boxplot entirely above zero indicates that the enacted plan cracked Democratic voters in that district.Source: §5 · p. 14
  • Simulated partisan outcomes differed unpredictably across data sources; DAS erased Census-indicated cracking and reversed packing in South Carolina, while Pennsylvania Democratic districts shifted by up to five percentage points.The South Carolina State House showed cracking disappear in districts 61–75 and packing reverse in districts 111–115 under DAS-4.5.Source: Figure 6 · p. 13, §5 · p. 14
  • District-level discrepancies can change conclusions about whether a partisan gerrymander is present, and their inconsistency within a state complicates research and decision making.Redistricting litigation often focuses on a single district or set of districts.Source: §5 · p. 14

6 Racial Effects on Redistricting

DAS data alter racial packing and cracking patterns in some districts, though effects vary across states and district sizes. Stronger constraints encouraging majority-minority districts also increase precinct-level differences in district-assignment probabilities.

6 Racial Effects on Redistricting

  • Racial packing or cracking patterns disappeared or reversed in South Carolina State House districts under DAS, while congressional district racial makeup in North and South Carolina appeared unaffected.The South Carolina State House patterns included districts ordered 121–124 and 96–110.Source: §6 · p. 14, Figure 7 · p. 15
  • In Mississippi State Senate districts 49–52, packing became cracking under DAS-4.5; Pennsylvania districts 16 and 17 also showed differences across data sources.Pennsylvania’s 14 most White congressional districts were generally stable, while heavily non-White districts 16 and 17 differed by as much as seven percentage points.Source: §6 · p. 16
  • With no VRA constraint, precincts had similar majority-minority-district probabilities across datasets; stronger constraints systematically altered individual precinct assignments.Some precincts were never assigned to an MMD under one dataset but always assigned under another.Source: §6 · p. 16, Figure 8 · p. 16

7 Ecological Inference and Voting Rights Analysis

The section evaluates BISG race imputation using Census and DAS data, then examines how differences affect redistricting analysis in East Ramapo. DAS-based predictions can undercount majority-minority districts in that case, while statewide prediction accuracy remains similar to Census-based accuracy.

7.1 Prediction of Individual Voters’ Race and Ethnicity

  • BISG combines voter names with Census block-level racial composition to impute race, using name likelihoods and geographic racial priors in a Bayesian calculation.The evaluation compares geographic priors from the 2010 Census and DAS datasets against self-reported voter-file race.Source: §7 · p. 17, §7.1 · p. 17
  • AUROC may not capture DAS-related attenuation of individual race probabilities, even when overall classification performance is maintained.The authors describe the strong DAS performance in this setting as counter-intuitive and offer possible explanations rather than a settled cause.Source: §7.1 · p. 18
  • Using highest-probability classification, misclassification rates are 15.1%, 12.1%, and 10.0% for Census priors, versus 15.1%, 12.0%, and 9.9% for DAS-12.2.The three rates correspond respectively to last name; last and first names; and last, first, and middle names.Source: §7.1 · p. 18
  • For the three main racial and ethnic groups, DAS-based voter-race predictions appear as accurate as 2010 Census-based predictions, although individual predictions can change.AUROC slightly improves with DAS-12.2 and slightly degrades with DAS-4.5 for groups except Hispanics; both DAS datasets slightly improve Hispanic predictions.Source: §7.1 · pp. 18–19

7.2 Ecological Inference in the Voting Rights Analysis

  • DAS-12.2 imputation tends to assign blocks more White registrants and lower Black and Hispanic shares, especially where either group forms a majority.The precise cause is unclear; the authors suggest differential noise and its propagation through nonlinear racial imputation may contribute.Source: §7.2 · pp. 19–20
  • In 10,000 East Ramapo plans, 56% of plans estimated to have 2 majority-minority districts under Census data were predicted to have only 1 using DAS-12.2.The study reports that DAS-12.2 never estimated more majority-minority districts than Census data across the simulated plans.Source: §7.2 · p. 20, Table 2 · p. 20
  • The East Ramapo case does not establish a general direction or magnitude of racial effects; these depend on DAS tuning and geographic factors.The authors caution against extrapolating from this single case study, while noting that small electoral districts may experience bias favoring one racial group over another.Source: §7.2 · p. 20

8 Conclusion

Using the 2021 demonstration data, the paper finds that treating DAS-protected counts as-is can distort redistricting and voting-rights analyses. The authors identify privacy-accuracy trade-offs, including population-parity errors and continued ability to predict individual race.

8 Conclusion

  • DAS noise shifts counts from racially heterogeneous and mixed-partisanship areas toward more homogeneous areas, producing large, unpredictable district-level biases, especially for small districts.The authors say these biases can affect partisan and racial outcomes in upcoming redistricting.Source: §8 · p. 21
  • DAS noise can make it difficult or effectively impossible for states to meet current One Person, One Vote population-parity standards.The reported population deviations can be several times larger than the DAS figures indicate, with greater problems for smaller districts.Source: §8 · p. 21
  • The post-processing obscures the source of these biases; the authors suggest racial-group accuracy targets and lack of block-level prioritization may contribute.Precinct-level DAS-12.2 counts averaged about 1% deviation from 2010 Census counts, and errors did not always cancel out.Source: §8 · p. 21
  • Because post-processing makes statistical adjustment difficult for common models, analysts may treat DAS data as-is; releasing unprocessed noisy data could help calibrate uncertainty, but would not fix map drawing.The authors also say new methods are needed to incorporate DAS noise in redistricting simulations, and its effect on power to detect gerrymandering remains uncertain.Source: §8 · p. 21
  • Race prediction from names and addresses in a public voter file was as accurate with DAS data as with the original Census data.The authors caution that accurate prediction does not necessarily constitute a differential-privacy violation, but argue it matters when weighing privacy benefits and costs.Source: §8 · pp. 21–22
  • The authors frame privacy protection as a trade-off with Census accuracy and argue that its burden should not fall disproportionately on particular racial or political groups.The Census collects basic demographic information such as race, which supports redistricting and public-policy decisions.Source: §8 · pp. 21–22

9 Postscript

The finalized DAS-19.61 demonstration data improve some population-count errors but do not resolve problems relevant to redistricting. Biases and simulation differences persist at the VTD level, and race prediction remains accurate relative to 2010 Census data.

9 Postscript

  • The latest DAS release improves many earlier results but leaves redistricting problems unresolved, including substantial VTD-level biases that may persist regardless of privacy-budget increases.The Bureau increased the privacy loss budget to 19.61 and changed post-processing; errors at some smaller geographic levels may rise as higher-level errors are reduced.Source: §9 · pp. 22–23

9.1 Racial and Partisan Biases

  • VTD-level racial and partisan bias remains, at about half the earlier magnitude, although the earlier racial biases were largely eliminated for on-spine geographies.Congressional-district deviations in studied states narrowed from –2,153 to 2,164 under DAS-12.2 to –216 to 319 under DAS-19.6.Source: §9.1 · p. 23

9.2.1 Population Parity in Redistricting

  • Strict parity goals can still yield invalid plans under DAS-19.61, though the enacted Louisiana map remains valid at a 5% intended tolerance.The chance of a plan exceeding its intended parity goal increases as the tolerance is lowered.Source: §9.2.1 · p. 23

9.2.2 Partisan Effects on Redistricting

  • DAS-19.61 partisan simulations differ from Census-based results by several percentage points in some districts, enough to shift the direction of measured partisan bias.The reported examples include Pennsylvania district 15 and South Carolina State House districts 111–115 and 121–124.Source: §9.2.2 · p. 24

9.2.3 Racial Effects on Redistricting

  • Racial simulation results remain problematic in districts that diverged under earlier releases; some precincts appear in majority-minority districts under Census data but never under DAS, or vice versa.The authors suspect simulations are sensitive to noisy VTD-level assignments because they repeatedly calculate from and reassign individual VTDs.Source: §9.2.3 · p. 24

9.3 Ecological Inference and Voting Rights Analysis

With DAS-19.61, individual voter race and ethnicity prediction remains nearly as accurate as with the 2010 Census data. In the East Ramapo school-board case, however, DAS-based estimates still undercount minority voters and majority-minority wards.

9.3.1 Prediction of Individual Voters’ Race and Ethnicity

  • DAS-19.61 predicts individual voters’ race and ethnicity with almost identical accuracy to the 2010 Census data, with no significant degradation in classification quality.BISG performance is generally similar for White and Black voters, slightly better for Hispanic voters, and slightly worse for Asian and Other voters.Source: §9.3.1 · pp. 24–25

9.3.2 Ecological Inference in the Voting Rights Analysis

  • In East Ramapo, DAS-19.61-based estimates overstate White voters and understate Black and Hispanic voters, with sampled majority-minority wards always underestimated.The block-level minority-voter undercounts persist at the school-board ward level.Source: §9.3.2 · p. 25

A Prediction of Individual Voters’ Race and Ethnicity: Accuracy Tables

The appendix reports voter-ethnicity classification error rates using different geographic priors and name-based predictors. Its tables describe error-rate measures and predictor configurations, but the supplied passages provide no table values.

A Prediction of Individual Voters’ Race and Ethnicity: Accuracy Tables

B Undercounting Bias with DAS-4.5 Data

The appendix repeats three main-paper figures with DAS-4.5 data instead of DAS-12.2 to show that bias occurs across privacy-budget levels.

B Undercounting Bias with DAS-4.5 Data

C Empirical Results with the DAS-19.61

This section re-analyzes main-paper results using DAS-19.61 data, including findings on majority-minority district counts and precinct-level probabilities.

C Empirical Results with the DAS-19.61

  • The re-analysis maps DAS-19.61 figures to errors by race, heterogeneity, and Democratic vote, plus population parity and simulation analyses.Source: C Empirical Results with the DAS-19.61 · p. 30
  • Figure C4 compares the share of Louisiana Senate plans exceeding their intended population-parity tolerance under another data source; its dashed line marks the enacted map’s maximum deviation.The horizontal axis is the original tolerance on a log10 scale; the vertical axis is the percent of plans exceeding the intended tolerance under evaluation data.Source: Figure C4 · p. 32
  • Under stronger majority-minority-district constraints, precinct-level probabilities of assignment to such districts differ more from Census-based probabilities.Source: Figure C7 · p. 35
  • The supplement evaluates voter-race prediction using geographic priors, reporting AUROC and race-specific overall, false-negative, and false-positive error rates.Source: Figure C8 · p. 36, Table C1 · p. 37
  • Figure C9 compares block-level race imputations from 2010 Census data with imputations using DAS-19.61 data.The axes show the percent of a group under each data source’s most-likely-race imputation.Source: C Empirical Results with the DAS-19.61 · p. 30, Figure C9 · p. 37
  • DAS-19.61 data lead to undercounting majority-minority districts in many plans, but never to overcounting them.Source: C Empirical Results with the DAS-19.61 · p. 38
  • Table C3 summarizes differences in existing congressional-district populations under three DAS populations relative to the enacted map.For each state, it reports the minimum, median, maximum, and standard deviation of the differences.Source: Table C3 · p. 39
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