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LetterValidating the Applicability of BISG to Congressional RedistrictingKEVIN DELUCA Harvard Kennedy SchoolJOHN A. CURIEL MIT Election Data and Science Lab

E nsuring descriptive representation of racial minorities without packing them intodistricts is difficult in states that do not collect race data on their voters. Oneadvance since the 2010 redistricting cycle is the advent of Bayesian Improved

Surname Geocoding (BISG), which greatly improves upon previous ecological inferencemethods in identifying voter race. In this article, we test the viability of employing BISG tocreate efficient minority majority districts. We validate BISG through 10,000 redistrictingsimulations of North Carolina and Georgia’s congressional districts and compare BISGestimates to actual voter file racial data. We find that summing the BISG probabilities leadsto significantly lower error rates at the precinct and district level relative to the pluralitymethod of assigning race, and therefore should be the preferred method when using BISGfor redistricting. Our results suggest that BISG can help with the construction of efficientminority majority districts.

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INTRODUCTION

T he creation of minority majority districtsfor underrepresented racial minorities re-mains a key point of contention within

the field of redistricting and representation. Thereis the constant danger of “packing” racial mi-norities into too few districts and minimizingtheir influence within the legislature, or “cracking”racial minorities into districts with no represen-tatives of the same race. Striking the correctbalance is one of not only great theoretical con-cern, but also methodological. It is difficult toidentify the optimal racial composition of districtsthat avoids wasting the votes of racial minorities.Further complicating the problem is calculatingindividual-level turnout and vote preferences byrace given data aggregated to county or precinct

Kevin DeLuca is a PhD Candidate at the HarvardKennedy School: kevindeluca@g.harvard.eduJohn A. Curiel is a Research Scientist at the MIT

ElectionData and Science Lab. CorrespondingAuthor:jcuriel@mit.edu

This is a manuscript submitted for review.

levels. While voter file data on registration andturnout can help construct efficient minority ma-jority districts, many states collect no racial in-formation in their voter registration lists. Thecompounding uncertainty makes it necessary toerr on the side of packing districts with minorityvoters to ensure an acceptable number of minorityminority districts.

There have been a number of significant quan-titative advancements in the field of redistrictingsince the 2010 redistricting cycle that can assistin drawing efficient minority majority districts.In addition to the increasing accessibility of re-districting simulation techniques, the advent ofBayesian Improved Surname Geocoding (BISG)estimation of race is a promising development.BISG calculates the joint probability of racialmembership given an individual’s surname andgeographic residence, which could be used to as-sist in drawing minority majority districts in stateswhere race/ethnicity is missing from voter files.BISG methods have also become increasinglyaccessible and commonly used in various waysthroughout social science research (Clark et al.

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2021; Imai and Khanna 2016). In this letter, wevalidate the applicability of BISG in the context ofredistricting by estimating the error of BISG raceestimates relative to self-reported race data fromthe voter files of North Carolina and Georgia.

Within this letter, we first demonstrate therange of error in implementing BISG againstverified voter file race data. Second, we demon-strate the expected error given two methods toimplement BISG within redistricting: polygon-aggregated probability summed method estimates(PSM) versus individual level plurality method(PM) assignment. We estimate district-level uncer-tainty around BISGmethods by simulating 10,000congressional district plans for each state and com-pare BISG estimates of the racial composition ofdistricts to voter file data. BISG district-level esti-mates (using PSM) of the share of minority votersin districts typically fall within 5 percentage pointsof self-reported voter file racial data, though themagnitude of the errors vary across states andracial groups. These findings provide a set of bestpractices and baseline estimates of uncertaintyfor researchers, lawyers, and legislators who wishto use BISG in the context of redistricting andsimulations.

REDISTRICTING AND RACEFrom a representational perspective, ensuring theelection of racial minorities through redistrict-ing is of special import. Historical oppressionand racism against racial minorities, and African-Americans in particular, often led to districtswhere election of racial minorities was all but im-possible. The Voting Rights Act (VRA) providedthe legal inception of minority majority districtsthrough its non-retrogression and pre-clearanceprovisions (Lublin 1997). The advent of the VRAand states under pre-clearance all but banned thepractice of “cracking” racial minorities into sev-eral districts in an attempt to thwart their presencein legislative delegations (Cox and Holden 2011).

Despite gains during the VRA era for rep-resentation of racial minorities, it is difficult toknow the exact percentage of minority voters thatare needed for a minority majority district. Two

competing and justified concerns exist regardingminority majority districts. First, if racial minori-ties and their electoral coalition partners numbertoo few, the district plan “cracks” racial minori-ties into several districts, where racial minoritiesare unable to elect a member of their preference.Second, if racial minorities and their coalitionpartners number too many, they will be able toelect a member of their preference, though atthe expense of a broader array of allied mem-bers within the legislature, victim to “packing”or “bleaching” as it’s commonly known (Grose2011; Lublin 1997). Both cracking and packinglead to racial vote dilution and are forms of ille-gal racial gerrymandering, though it is easier forredistricting plans to legally justify the practiceof “packing” (Cox and Holden 2011).

Cameron et al. (1996) finds that the "optimal"plans for maximizing black representation in theSouth uses minority majority districts that are47% black voting age population districts, but thatmany minority candidates have a good chanceof winning in districts that are lower than 50%minority in racial composition. Grose (2011)identifies a threshold at or below 25 percentAfrican-American as nigh impossible to electa black member. Hicks et al. (2018) find theprobability of electing a black member to the leg-islature in a district where just under 50 percentof the district population is black plummets tonear zero in the Deep South. Lublin (1997) notesthat minority-influence districts might be a moreefficient way to ensure substantive representationof racial minorities through the election of bothmore racial minority members and Democrats, yetrecent research suggests these can easily backfire.

Legislatively and legally, there are often dis-putes over howmanyminority voters are needed ina district in order to create minority majority dis-tricts or minority-influence districts. Republicansoften like to over pack minorities into districtswhile Democrats like to create a higher number ofminority-influence districts, due the partisan ef-fects of each outcome (Bullock III 2018). Until theShelby1 decision in 2013, the non-retrogression

1Shelby County v. Holder, 570 US 529 (2013)

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provisions of Section 5 of the VRA also pushedmapmakers to err on the side of keeping minorityvoters packed into districts, as to not degrade ordilute existing minority majority districts (Bul-lock III 2018; Cox and Holden 2011). In practice,this means that redistricting generally tends packtogether too many racial minorities rather thantoo few (Cox and Holden 2011).2

Confounding the substantive question of re-districting and race is a methodological one: howdoes one actually measure racial preferences andturnout given the Census demographics at thestart of the decade so as to ensure a not over- orunder-packed minority majority district? Suchquestioning is the basis of Ecological Inference(EI) methodology, where the goal is to estimateboth the electoral turnout by race and electoralpreference of those who turn out given the demo-graphics of an area (Goodman 1953; King 1997).Using Citizen Voting Age Population (CVAP)alone does not account for differential levels ofregistration or turnout rates across racial groups,both ofwhich can significantly affect racialminori-ties’ political influence. Recent evidence suggeststhat mapmakers target differential voter eligibilityand turnout when gerrymandering (Fraga 2015;Henderson et al. 2016). Even the best EI methodscoupled with on the ground qualitative researchare far from perfect, and often necessarily lead todistrict plans “erring” on the side of caution soas to prevent cracking (Grose 2011; Grose et al.2007; Hicks et al. 2018).

Using race data on voters contained in states’voter registration files to measure district-leveldemographics can aid in the creation of minoritymajority districts. Voter registration files containthe set of eligible and registered voters, and often

2So far we have largely discussed racial minorities asprimarily Democratic voters. There will be greatervariance among Hispanic and Asian/Pacific-Islandervoters, who tend to vote more Republican than AfricanAmericans (Masuoka 2006; Masuoka et al. 2019; Haj-nal and Lee 2011). As Hicks et al. (2018) show in theiranalysis of state legislators from the 1990s to the 2010s,over 96 percent of African-American legislators areDemocratic, with their bases increasingly relying uponcoalitions of African-American and Hispanic voters.

individual-level voter history. Therefore, it is pos-sible to estimate an individual-level likely turnoutmodel with a voter registration file, completelynegating one stage of EI. However, many states donot collect individual race data in their voter files –including states like Texas, Pennsylvania, andWis-consin, which are often subjects of contentiousgerrymandering litigation.

A promising innovation in the field of EIsince the previous redistricting cycle is the de-velopment of Bayesian Improved Surname andGeocoding (BISG) estimation of race. Imple-mented first in the field of public health by Elliottet al. (2008), BISG calculates the joint proba-bility of racial membership given surname andgeographic residence. Individually, surname andresidence are each susceptible to heterogeneouspriors/marginals but jointly they vastly reduce theerrors of even advanced EI methods (Imai andKhanna 2016; King 1997). Theoretically, BISGcould be used to assist in drawing minority ma-jority districts in states where voter race data ismissing orwhere differential voter registration andturnout rates across racial groups are not reflectedin Census estimates of district demographics. Todate, however, there has been no research vali-dating the extent to which BISG methods can beused to construct accurate estimates of the racialcomposition of proposed districts. Given the ob-vious application of BISG to redistricting yet itsuntested veracity, we aim to estimate the range oferrors associated with BISG in redistricting andprovide best practices for those using BISG inredistricting work.

USING BISG IN REDISTRICTINGBISG uses an individual’s surname and locationto estimate their race via Baye’s rule (Elliott et al.2008; Imai and Khanna 2016). Using individu-als’ surnames matched to a surname dictionary,joined to Census geography demographics, typi-cally produces accurate racial estimates relativeto other methods (Imai and Khanna 2016). Whilethe errors tend to be greatest where the surnamesare uninformative and geographic units hetero-geneous by race (Imai and Khanna 2016; King

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Author One, Author Two, and Author Three

1997), BISG greatly reduces the number of indi-viduals afflicted by such uncertainty. So long assub-county units are employed, BISG racial esti-mates outperform alternative methods when veri-fied against states with racial information on theirvoterfiles, as shown by Imai and Khanna (2016)and Clark et al. (2021). The benefits and easeof use of BISG therefore earned its widespreaduse within political science, such as estimatingthe race of political donors (Alvarez et al. 2020;Grumbach and Sahn 2020), voters (Fraga 2015),and candidates (Shah and Davis 2017). Thesedevelopments in BISG, which were not availableat the time of the 2010 redistricting cycle, offeran opportunity for researchers and mapmakers tomore easily incorporate racial information in theupcoming redistricting process, and can facilitatethe drawing of minority majority districts that areneither overly packed with minority voters norlacking significant minority populations.

In terms of using BISG in redistricting re-search, the main question is ascertaining the de-gree of error given how the researcher assignsracial categories given BISG output. Clark et al.(2021) follow the practice of summing the esti-mated probabilities that an individual is of a givenrace up to the unit of interest, such as precinct.However, scholarship by Enos (2016) and Enoset al. (2019) assigns a single race to a voter giventhe racial category with the highest estimatedprobability. Plurality assignment goes againstbest practices within population level social sci-ences (King 1997) given the potential for extremeand clustered errors. Normally, plurality assign-ment of race would not be considered. However,it is foreseeable that one might apply pluralityassignment to redistricting. Following the redis-tricting revolution of “one person, one vote,” itis necessary to often split precincts in order toensure literal population equality across districts(Cox and Katz 2002; Grofman 1985). Partisanmotivated mapmakers might also prefer to cherry-pick individuals into other districts as a meansto break up personal constituencies and force op-posing incumbents into retirement (Cox and Katz2002). Therefore, the ability to assign individualsto a single category, if done accurately, offers

benefits tempting to redistricting practitioners andscholars.

BISG VALIDATIONWe validate the application of BISG to two stateswith racial information on their voter files, NorthCarolina and Georgia. These states also requireminority majority districts at the congressionallevel. We therefore first calculate the distributionof errors applying BISG to these states. Second,we evaluate both methods of BISG race assign-ment – the BISG probability sums method (PSM)and the plurality method (PM). Finally, we esti-mate the degree to which redistricting simulationsdistribute these errors relative to the voter regis-tration file in creating districts via the ensemblemethod of swapping districts from a seed mapwith the required number of minority majoritydistricts within each state.

For the purpose of implementing BISG, weuse the R package zipWRUext (Clark et al. 2021),which uses surname and ZIP code demographicsto calculate the joint probability of racial identifi-cation for individuals. This allows us to quicklyproduce accurate estimates of the predicted raceof each voter, without having to undergo a costlyand time-consuming geocoding process.3 Weperform diagnostics on the individual-level raceBISG predictions in Appendix B, where we cal-culate the effective number of races, which is theinverse of the Herfindahl index (Clark et al. 2021;Wolak 2009). Appendix B demonstrates that inmost cases the BISG estimates range between

3Geocoding millions of voter addresses can take weeksand cost thousands of dollars, which often presentsan obstacle to utilizing BISG for those without largeresearch budgets. In contrast, when using ZIP codes(which are available in all voter files which containvoter addresses that would be necessary for geocoding)as the BISG geography it takes about 10 minutes toproduce race estimates for 7 million voters in theGeorgia voter file, on a 3.1GHz MacBook Pro with8GB of RAM. See Clark et al. (2021) for details anddiscussion of the relative advantages of using ZIPcodes rather than geocoded Census block or tractinformation.

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FIGURE 1. BISG Precinct-Level Error Density Plots(a) White - North Carolina (b) White - Georgia

(c) Black - North Carolina (d) Black - Georgia

one and two effective races. Next we estimatethe proportion of black and white voters usingboth the PM and PSM assignment procedures.These estimates are benchmarked to the actualself-reported racial data within the voter files.

Figure 1 shows a density plot of the precinct-level errors in racial estimates, calculated as theabsolute percentage difference from the reportednumber of voters for both North Carolina andGeorgia, by race. Forwhite voters, themodal errorapproaches zero for both assignment methods,though PM has a longer right tail, which indicatesworse performance relative to PSM. For blackvoters, PSM also outperforms PM in reducingprecinct-level errors, vastly so in this case. Arecommendation we make confidently from justthese precinct-level results is that PSM should bethe preferred method when estimating the racialcomposition of precincts using BISG on voterfiles.

REDISTRICTING SIMULATIONS

To evaluate the accuracy and uncertainty of BISGestimates of race at the district level, we perform10,000 redistricting simulations each of North Car-olina and Georgia’s congressional district mapsusing the Redist package in R (Fifield et al. 2020),version 2. The Redist package makes use of en-semble methods, useful in estimating ranges ofexpected outcomes (Katz et al. 2020). We crafta basemap from the precinct simplified map em-ployed by Curiel and Steelman (2018) for NorthCarolina, and a modified map of the plan imple-mented inGeorgia following the 2010 redistrictingcycle. We then proceed to simulate districts viarook contiguity. For each simulated plan we cal-culate the absolute percentage point differencebetween the estimated proportion of each race ineach district and the actual proportion using thevoter file data. This allows us to calculate theerror rates for the BISG PM and PSM at the con-

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FIGURE 2. BISG District-Level Error Sensitivity - North Carolina and Georgia(a) Percent White - North Carolina (b) Percent White - Georgia

(c) Percent Black - North Carolina (d) Percent Black - Georgia

gressional district level. We use our simulationsto create a 95 percent confidence interval aroundthese estimates.

The error rates and confidence intervals forNorth Carolina and Georgia are plotted in Figure 2for both white and black voters. The x-axis sortscongressional districts in order of increasingwhitepercentage when plotting the absolute error forwhite voters (plots a and b), and in order ofincreasing black percentage when plotting theabsolute error for black voters (plots c and d). Innearly all district-level estimates, PSM results insignificantly lower absolute error rates relative toPM, consistent with the precinct-level diagnostics.

While the error rates are relatively low ingeneral, they vary both across states and acrossracial groups. In North Carolina, the absoluteerror for BISG probabilities are close to zero forthe percentage of white voters in each district,and never go above five percentage points for the

percentage of black voters in each district. InGeorgia, the error rates are slightly higher – forwhite voters, they max out around 10 percentagepoints, but for black voters the error rates arelower and, like North Carolina, peak around 5percentage points. Overall, plurality assignment(PM) substantively increases errors relative tosumming the estimate probabilities (PSM).

DISCUSSIONAs simulations become more common in redis-tricting (Fifield et al. 2020), and as the next re-districting cycle approaches without the previousprotections of VRA preclearance, BISG has thepotential to easily provide researchers with a wayto construct minority majority districts efficiently.This can be especially useful in states where voterrace data is missing from the voter files. Our letterperforms the first empirical validation of BISGuse in redistricting, and provides a set of simple

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recommendations and guidelines for researchersthat use BISG in redistricting analyses.

First, researchers using BISG should aggre-gate up to some polygonal unit of interest bysumming the estimated probabilities of racialmembership. Although it might be tempting toassign race to single voters in order to aid inpoint-based redistricting attempts, the errors willbe drastically higher, reducing the usefulness ofBISG. While there might be occasions to fol-low the practice of plurality assignment of race,redistricting is not one of them.

Second, researchers should be prepared todeal with around a five to ten percentage pointerror rate in estimating race at the district level.In states where voter race is not collected, BISGoffers a fairly accurate workaround. However,context matters. Insofar as electoral preferencescan be divided between white and non-white cat-egories, such as the drawing of coalition districts,BISG reaches high levels of accuracy. However,when researchers need to estimate the district com-position of a specific racial minority group, suchas Blacks or Hispanics, the potential for greatererror should be considered.

Finally, it is possible to achieve these BISGestimates at relatively low cost via modern BISGpackages in programs such as R. Imai and Khanna(2016) greatly expanded the ease of integratingCensus data and surname dictionaries for BISG,and Clark et al. (2021) demonstrate the ability toattain accurate estimates while avoiding the needto geocode altogether with ZIP codes. Therefore,it is possible to provide accurate race estimatesfor millions of voters in just a couple of minutes.While there is heterogeneity in the errors associ-ated with BISG, keeping such limitations in mindcan allow the user to adjust accordingly.

Future work should look at the accuracy ofBISG and redistricting in terms of non-black racialminorities. In Texas, for example, the creation ofmajority-Hispanic districts is a common redistrict-ing controversy. Other work can and should tryto incorporate BISG estimates with differentialturnout across racial groups from voter history(which is often contained in voter files) to createminority majority district. Further research is

also needed to better understand what tempersthe effectiveness of BISG in different contexts.Clark et al. (2021) noted that ZIP code BISGworks better for black and white voters than forHispanic or Asian voters, but more could be doneto understand the contextual factors that affecthow accurate BISG estimates of legislative dis-tricts will be when aiming to create and evaluateminority majority districts. The uncertainty inour estimates for North Carolina and Georgiashow that while BISG is fairly accurate in gen-eral, better understanding the sources of error inthe data can further improve BISG’s usefulnessin redistricting and its general applicability tosimulation methods. Additional Bayesian priorsmight additionally be implemented into existingBISG packages to allow for greater uncertainty,especially for contexts where it is not possible tovalidate the final results.

Legislators, researchers, and everyday citizenswill have access to a whole new set of quantitativetools in the 2020 redistricting cycle. Many of thesetools and new methods are aimed at reducingpartisan and racial biases in maps in order topromote more fair and equal representation. Butthese tools andmethods can still produce biased orinefficient districts if, for example, voter race dataitself is unrepresentative of the actual electorate.Our letter helps to reduce the errors in estimatingaggregate racial data, and can assist mapmakersusing these new quantitative tools create efficientminority majority districts.

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APPENDIXDATAShapefiles for precincts come from the Census Bureau’s Tigerlines data set of tabular blocks.4 Weemployed the Census block data to estimate the total population for the purpose of weighting precinctswith population data for redistricting simulations, and census estimates of race. We assigned blocks toprecincts conditional upon where its geographic centroid was located (Gimpel et al. 2006). We acquiredthe precinct data for North Carolina from the North Carolina State Board of Elections (NCSBE) precinctmap archive5 and the voter file from the archive snapshots from the NCSBE.6 We attained a precinctmap from the Open Precincts project site for Georgia7. We purchased the entire Georgia voter file inDecember of 2020 for $250 on the Georgia Secretary of State website.8. Georgia’s voter file exhibitedmismatch between the precinct IDs within the voter file, so we therefore geocoded every address usingthe ESRI 2013 classic geocoder suite, and overlaid ensuing point shapefile onto the precinct shapefile.

DIAGNOSING BISGIn order to diagnose the precision of the BISG estimates at the individual level, we display densityplots of the uncertainty in BISG estimates, separately for both North Carolina (a) and Georgia (b)in Figure B1. On the x-axis, we plot the effective number of races, the inverse of the Herfindahlindex (Wolak 2009; Curiel and Steelman 2020). Overall, there is a global mode at approximately oneestimated racial grouping. However, there are local modes at around two effective races, suggesting asubstantive level of uncertainty in the estimation of racial categorization. Figure B2 and Figure B3 plotthe average error rates separately for white and black voters based on the effective number of races, inNorth Carolina and Georgia, respectively, and confirm that as BISG uncertainty increases so does theaverage error.

4U.S. Census Bureau. 2010 Census Tallies of Census, Tracts, Block Groups, and Blocks. (last up-dated March 26, 2012), https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.2010.html (accessed October 10, 2020).5“Precinct Maps, 2012.” North Carolina State Board of Elections. (last updated February 8, 2016), https://dl.ncsbe.gov/?prefix=PrecinctMaps/ (accessed February 17, 2021).6“Voter registration snapshots.” North Carolina State Board of Elections, November 6, 2012. (last updatedMarch 2, 2017). https://dl.ncsbe.gov/index.html?prefix=data/Snapshots/ (accessed February 17,2021).7Georgia. Open Precincts. <https://openprecincts.org/ga/> (accessed February 22, 2021).8Voter list. Georgia Secretary of State. https://georgiasecretaryofstate.net/collections/voter-list-1 (accessed December 1, 2020).

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FIGURE B1. Precision of Individual-Level BISG Estimates(a) North Carolina

(b) Georgia

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FIGURE B2. Errors by Heterogeneity - North Carolina

FIGURE B3. Errors by Heterogeneity - Georgia

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