Background & Summary

Ballots are the core records of elections. While the total counts of ballots for individual candidates are reported regularly1,2,3,4, individual ballots are rarely made available.

In paper-based elections, three types of records at the individual ballot level have been available to some researchers and litigators. The first is the actual, marked paper ballot. The second is the electronic scan of the paper ballot, often referred to as a ballot image. The third is an electronic record of the machine’s interpretation of that scanned record, called cast vote records (CVRs, Fig. 1). The National Institute of Standards and Technology describes CVRs as “an electronic record of a voter’s selections, with usually one CVR created per sheet (page) of a ballot.”5. CVRs are not the ultimate basis of an election, but because “election results are [often] produced by tabulating the collection of CVRs”5, they should directly reproduce vote totals produced by ballot tabulators. Among the three types of records, CVRs lend themselves best for analysis.

Fig. 1
figure 1

Cast Vote Record Example. An example of an actual ballot image (left) and the authors’ representation of the associated cast vote record (right) in Wisconsin. Blank marks are recorded as an undervote.

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In this study, we introduce a dataset of CVRs representing 42.7 million voters. The dataset is available on the Dataverse at https://doi.org/10.7910/DVN/PQQ3KV6. Unlike certified election results–typically made available by state election officials–CVRs are rarely centralized at the state level. Instead, CVRs are often produced as a byproduct of the tabulation process conducted at the sub-state level and retained by local election officials.

Following the November 3, 2020 U.S. general election, local election officials saw a surge in requests for cast vote records by anonymous constituents. Some states saw a four to five-fold increase in records requests between 2020 and 20227,8. Owing to the work of election administrators in responding to these requests, and to O’Donnell for posting those unprocessed records online9, researchers now have access to an unprecedented quantity of cast vote records. O’Donnell and his collaborators originally collected the CVRs in order to investigate the validity of the 2020 presidential election10 (to evaluate these claims, we refer readers to work by other researchers11). We standardized the publicly available CVRs into a single database, and extensively compared them to official election results.

Our final dataset has two main audiences. The first audience are those in political science, economics, sociology, and other related fields who study electoral behavior. CVR data will allow researchers to study a wide variety of electoral phenomena. In particular, it will allow researchers to measure important aspects of voting behavior much more accurately than is possible using aggregate election returns or surveys. The CVRs are at the individual level and record voters’ actual choices across multiple offices. For example, the CVRs include choices for state legislative races. These are rarely included in surveys because researchers typically focus on top-of-the-ticket races. Moreover, survey estimates of vote choices in down-ballot elections can result in especially large measurement errors because respondents are less likely to correctly recall who they supported in down-ballot elections. Such estimates may have especially large sampling errors too, because only a few respondents in a typical nationally representative sample will have participated in any particular down-ballot contest such as those for state legislative seats.

One important electoral phenomenon is split-ticket voting, that is, voting for candidates with different partisan affiliations across offices. For example, aggregate-level election data can tell us how many votes Donald Trump received in a state and how many voted for each of the Republican candidates for offices further down the ballot, but it cannot tell us how many voters who voted for Donald Trump for President also voted for the Republican candidate on all the other (down-ballot) offices12,13,14. CVRs allow researchers to measure this type of behavior precisely, and at different levels of government, e.g., national level, state level, and across levels15,16,17. Researchers can also use CVRs to count the number of voters who vote for Democratic candidates and also vote for the progressive position in referendums18,19,20.

The data include geographic identifiers: counties and often precincts. One application possible with CVRs is to measure which state legislative or congressional districts have an especially high share of split-ticket voters. To the degree that these voters can be viewed as “swing” or “persuadable” voters, while straight-ticket voters can be viewed as “core” or “loyal” partisan voters, this measure could be used to test theories of resource allocation and campaign strategies21,22,23.

Researchers can of course merge the CVR data with other information about the candidates and contests, such as incumbency status, patterns of campaign spending, and candidate attributes, such as race, ethnicity, gender, ideology, and/or experience24. With this extra data in hand, researchers can begin to study a wide variety of phenomena, including which voters split their tickets and in which ways as a function of the available choices. They can also study the degree to which split-ticket voting favors incumbents or candidates who have a fundraising advantage17. Researchers can also merge the CVR data with precinct-level demographic and socio-economic information to explore relationships between split-ticket voting and these types of variables. For example, does ticket splitting vary with the types and amounts of media (e.g., local newspapers) available in an area25?

The CVR data could be used to study other electoral phenomena as well. For example, CVRs for contests featuring ranked choice voting allow researchers to analyze a voter’s preferences over all candidates26,27. Or, consider roll-off, where voters cast ballots but choose to abstain in particular races (also called undervoting). Using the CVRs, researchers can measure this behavior accurately. They can then investigate the types of races where this behavior is more prevalent, and the types of voters (e.g., straight-ticket Democrats, straight-ticket Republicans, or ticket-splitters) that are more likely to roll-off, as well as the interaction between contest and voter types. One final example is voting for candidates of minor parties, such as the Libertarian Party and the Green Party. Since the CVR database has millions of records, it contains many thousands of records of individuals who supported minor parties that received a small fraction of the vote28. The typical survey is less useful for studying this type of behavior due to sample size.

The second audience are those in election law, forensics, and administration, who seek to study the integrity of the electoral process29,30. Cast vote records are of interest to scholars of attitudes towards election integrity because voters’ mistrust of the vote counting process, when it exists, often revolves around the ballots31,32,33. Ballot-level data have been used in studies of election administration to help explain seemingly surprising election results34,35. Our dataset can also contribute to debates around the tradeoff between transparency and privacy36,37,38,39.

Finally, our data has implications that go beyond the particular states in this release, or even the 2020 election in particular. The November 2020 election was a turning point in U.S. politics, where the administration of elections became an overtly partisan issue. The conduct and administration of any other future elections now risks being politicized. Self-enforcing the legitimacy of elections requires election administrators, data scientists, lawyers, and social scientists to work together upon a common understanding of election technology. We hope that our data release serves as a standard for future work in this area of growing interest.

Methods

Out of 3143 counties in the U.S., votedatabase.com releases data from 464 individual counties and 3 statewide data sets (Alaska, Delaware, and Rhode Island). As described by O’Donnell9, this website provides access to the raw electronic files containing CVRs that were acquired by numerous citizens via open records requests. Of the 467 files, we validate and release 362 counties in 20 states. We additionally modify precinct information from 0.003% of the data for privacy protection. Privacy and our technical validation are discussed in more detail below.

We approached the raw data cautiously. CVRs may not include all of the ballots cast in an election for a number of reasons. Even within a single county, it is possible that some valid ballots are cast and tabulated in a way that creates CVRs while others are not. Sometimes ballots that are held aside for manual adjudication, such as provisional or damaged ballots, are not scanned through tabulators, and therefore a cast vote record is not created for such ballots. We can increase our confidence that CVR files posted are complete, uncorrupted, and genuine by comparing vote tallies produced using the downloaded CVR data to the official reports of vote totals from the same jurisdictions. Note that our goal is not an audit of the election. CVRs are neither sufficient nor necessary to rule out election malfeasance. While CVRs are convenient representations of the paper ballot, they are simply not intended to be the official results of an election. On the other hand, even if the cast vote record were complete, ballots could have been tampered prior to tabulation.

We start with data that O’Donnell and his collaborators obtained and subsequently uploaded to votedatabase.com9. O’Donnell reports that citizens requested CVRs according to their state’s open record law guidelines, noting that all records were “obtained through these valid public records requests”9. He reports that requests were sent to “nearly all counties in all states,” but 23 states responded that they did not have any records relevant to the request that could be provided under the state’s open records law (Alabama, Connecticut, Hawaii, Indiana, Kansas, Louisiana, Maine, Massachusetts, Mississippi, Missouri, Montana, Nebraska, New Hampshire, New York, North Carolina, North Dakota, Oklahoma, South Carolina, South Dakota, Utah, Virginia, Washington, and Wyoming). Indeed, the availability of CVRs is limited by state law and executive order, with states including North Carolina, South Carolina, and New York shielding the CVR from open records requests39. In all, the CVRs in the data presented here originate from counties in 27 states and D.C. that were collected and made available by O’Donnell9. The database contains data from swing states like Wisconsin, Michigan, and Georgia, as well as solidly Democratic states, including New Jersey, and solidly Republican states, including Texas.

Our standardization and validation proceeded in five steps. First, we downloaded the data files and standardized them so that their values were comparable across different voting machines and jurisdictions. While the website does provide some normalized versions of the raw data, we have chosen not to rely on these and instead independently process the raw data. We only considered files that were clearly CVRs in machine-readable form covering multiple offices and more than a handful of precincts. Standardization here entails that we identify the party affiliation of each candidate, code invalid votes consistently across jurisdictions, and standardize the formatting of candidate names. In the initial phase of the study, two groups conducted these pursuits independently, without awareness of each other’s work. This gave us nearly independent measures of inter-coder reliability and reduced the possibility that a single coding error propagated to all counties.

About 15 percent of the counties had CVRs in non-rectangular formats such as JSON or XML. The remaining files were tabular files such as CSV or Microsoft Excel. Formats differed by the vendor of the machine (the main three being Dominion, Hart Intercivic, and ES&S), and the make of each machine. For information about the particular machine used in each county, see https://verifiedvoting.org/verifier. We parsed these data with our own R and Python scripts, eventually normalizing all data into a long format where one row represents a single vote choice by a voter. This article releases the full codebase we developed.

Second, we assigned a cast vote record identifier to each voter, within a county or jurisdiction. Most times, this number indicates an individual voter–one anonymous voter gets one identifier for all their choices. In about 30 counties with ballots spanning multiple double-sided pages, each page was separated before it was scanned. Note that from the administrator’s perspective, once the ballot itself is deemed valid, the identity of the voter is irrelevant in the counting process. In about 20 of these counties, we used metadata to link pages into a single ID (see Supplementary Information A). In the remaining 10, the records were irreversibly separated. This includes several counties in California (Los Angeles, San Francisco, San Bernardino, Ventura Counties). Thus, in the vast majoriy of counties we study, there is a one-to-one correspondence between the ID we assign and a single  anonymous voter. Even in many counties with long ballots such as Maricopa, Arizona (with around 60 contests per ballot), the ballot record for each individual voter is preserved.

Third, we extensively checked the CVRs against other official sources of data, mainly the MIT Election Data and Science Lab (MEDSL) 2020 precinct-level returns3,40. This was an ideal dataset to use as validation because it is at the precinct-level, it has standardized its formatting across states, it includes district-level as well as statewide contests, and features extensive documentation. We limited our attention to six offices: U.S. President, Governor, U.S. Senate, U.S. House, State Senate, and State House. The CVRs include votes for many other offices, including local administrative offices, school boards, and referendums. Other work analyzes these offices15,16 but we exclude them in this dataset because we lack fully standardized official data to extensively validate against. After attempting to find the best matching official result for all counties, we only release counties with candidate-level discrepancies of 1 percent or less at the candidate-county level. The section “Technical Validation” discusses the process in more depth.

Fifth, we extracted precinct information in the cast vote records and standardized them to match MEDSL’s database of standardized precinct names. Precinct identifiers were often either names (e.g., “City of Madison Ward 1”) or numeric codes (e.g., Precinct 35-001). These classifications are known to vary widely across jurisdictions and machines, with no national standard. We used fuzzy string matching and triangulation of vote counts to link the precincts, which we detail in Supplementary Information B. There are 312 counties which we matched to the precinct level database.

Data Records

Our dataset includes 166,470,734 rows, with each row indicating a choice of a voter for a given contest. Our data is deposited in Dataverse at https://doi.org/10.7910/DVN/PQQ3KV6.

Variables

Table 1 describes the variables in the data. Voters are uniquely identified by the state, county name, and cvr_id assigned by ourselves, with the exception of unmerged fragmented ballots described in the methods section. Contests are uniquely identified by the state, office, and district. The names and values for our variables generally follow the naming conventions of the MIT Election Data and Science Lab3.

Table 1 Dataset Variables.
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The candidate value is the name of the candidate that ballot was cast for, or it can be an undervote (UNDERVOTE), overvote (OVERVOTE), or write-in (WRITEIN). Undervotes refer to a blank choice for that contest or mark that the tabulator could not interpret, and overvotes refer to a voter marking more candidates than they could vote for in a given contest. Even though both types of votes are invalid, undervoting in particular is seen as a form of contest-specific abstention and is of interest to election scholars.

In all offices but the State House in Arizona and West Virginia, the contests represented here are single-choice elections (a magnitude of one). Arizona voters can cast up to 2 valid votes to elect their Representatives for the state’s lower chamber, with 2 winners per district. Until 2022, West Virginia voters in some districts could cast up to 2 or 3 valid votes for their lower chamber.

Third-party candidates and write-in candidates rarely win themselves, but the ideological orientation of voters who vote for them is of interest to researchers28. When a candidate is listed on the ballot with a registered party, they are listed with their party affiliation in the party_detailed variable (such as Libertarian, Green, or “No Party Affiliation” in Florida). The party_detailed variable is set to missing for undervotes and overvotes. Jurisdictions vary in whether write-ins are reported separately or grouped together simply as write-in votes. Ballot access for third parties also varies by state. When the candidate is not listed on the ballot with a party, we record them as write-in candidates with no party affiliation (For more details, see Supplementary Information C).

Our dataset also records the precinct of the cast vote record, as discussed in the Methods section. We provide two variables for precincts (Table 1). precinct_medsl is our matched precinct name, formatted to correspond exactly with those described by Baltz et al.3. precinct_cvr is a concatenation of the original precinct or precinct portion name as it appears in the cast vote record by the pipe character |. The concatenation occurs for every set of precincts for a given precinct_medsl. For example, if precinct 001 as defined in the MEDSL precinct data3 contains two precinct portions 001A and 001B, and the cast vote records record the precinct portion, we give all voters in precinct 001 the value of 001A | 001B.

Privacy considerations

For certain vote records, we further aggregate the values of precinct_cvr and precinct_medsl by concatenating additional precinct portions and by concatenating two or more MEDSL precincts. In those records, the precinct_cvr and precinct_medsl fields indicate that the vote was cast in one of the listed precincts, but not which one. We apply this additional aggregation to avoid facilitating the linkage of any particular voter to a vote that they cast.

To understand how highly-disaggregated election results can reveal the vote choices of particular voters, suppose there is a precinct in which only 3 voters shared a particular ballot style. Here we refer to the ballot style as the subset of contests that the voter could vote on that are among the six we report. Who voted in U.S. elections is public via lists of voter rolls produced by election officials. Those voter rolls contain sufficient geographic information to infer the identity of each of these voters from their precinct and ballot style. If all of the voters in that precinct who used that ballot style supported the same candidate, the vote choice for those 3 voters would be revealed by the CVR data to anyone who has access to an accurate voter list39. While the release of CVRs might seem to increase opportunities for unraveling the secret ballot, nearly all of the information that can be used to reveal vote choices from the CVR data is already contained in the official precinct aggregates that counties commonly made public39.

If we reported the precinct_cvr and precinct_medsl fields without additional aggregation, as many as 5,391 votes choices out of 166.7 million vote choices (0.003%) contained in the database are considered revealed as defined by Kuriwaki, Lewis, and Morse39, i.e., can theoretically be linked to the voters who cast them, using the precinct and ballot style information contained in the database. We note that each of these 5,391 linkages is only theoretical because of practical data limitations that can sometimes make it impossible to infer the ballot style from the CVR or to construct a complete and accurate enumeration of every voter in a precinct who used a particular ballot style.

To address this potential linkage of votes to voters, we first compiled a list of precinct and ballot style combinations in which every voter supported the same candidate in at least one contest. In each of those instances, knowing who voted in the precinct using that ballot style is sufficient to learn one or more of the vote choices made by each of those voters. To avoid this revelation, we then pooled those revealed voters with voters from another precinct in the same county who used the same ballot style. In particular, each revealed precinct-ballot style voter combination was concatenated with the smallest precinct-ballot style voter combination in the same county that shared the same ballot style. For example, suppose the voters using ballot style A in precinct 001 had their votes revealed because all of them supported Donald Trump for President, and suppose precinct 002 had the smallest number of voters in the county among all non-revealed precinct-ballot style combinations using ballot style A. Then, we report the precinct value for voters using style A in both precincts as 001 | 002. Note that for other ballot styles used in precincts 001 and 002 (if any), there may be no vote revelations. For this reason, the database may contain records in which precincts 001 and 002 are concatenated (those associated with voters using ballot style A) and others in which they appear alone (those associated with voters using other ballot styles).

Geographic coverage

A total of 20 states are covered by our release. Figure 2 lists all counties in Version 2 of our released dataset.

Fig. 2
figure 2

List of Counties Released. For a spreadsheet version of this list, see file county_info.xlsx in our Dataverse repository. For a map of this list, see Supplementary Information D.

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We release all counties in the states of Nevada, Rhode Island, and Delaware after our procedure, while in other states, only a portion of the state’s counties is released. Table 2 compares the characteristics of our collected samples with the entire state. A convenient cross-state metric to indicate the representativeness of our release is the percentage of voters that vote for the Democratic presidential candidate, Joseph R. Biden. Table 2 compares the percentage of Biden voters as a share of Biden and Trump voters in the dataset and the state(s) as a whole. Overall, 56.6 percent of our collection’s Presidential voters are Biden voters (as a percentage of the two-party vote), while his two-party vote share in all 50 states was 52.2 percent41.

Table 2 Comparison of Data Coverage to Entire State.
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Table 3 compares the set of counties based on demographics. We take demographic data from the 2020 decennial Census at the county level and compare our counties with the entire United States. The Table reports the average and median value of each demographic variable, as well as the overall (population-weighted) value and the standard deviation. The population in our set of counties does not differ from the average U.S. county in terms of age or homeownership, but our counties are less White (52.8% vs. 61.2% nationwide), more Hispanic, and more urban.

Table 3 Characteristics of Counties Released.
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Technical Validation

We extensively analyzed each county’s files and compared them with official results, as described in the previous section.

Validation

In general terms, we define a discrepancy as any difference between the summed total of CVRs cast for candidates in the CVRs we processed from a county and the certified results published by that county. More precisely, we compute the discrepancy in a county k by the percentage

$${{\rm{d}}{\rm{i}}{\rm{s}}{\rm{c}}{\rm{r}}{\rm{e}}{\rm{p}}{\rm{a}}{\rm{n}}{\rm{c}}{\rm{y}}}_{k}={max}_{j\in {{\mathbb{I}}}_{k}}\left\{|\frac{{N}_{j}^{c}-{N}_{j}^{v}}{{N}_{j}^{v}}|\right\},$$
(1)

where Nc is the CVR vote count, Nv is the official vote count, j indexes candidates in a county, |·| is the absolute value function, and \({{\mathbb{I}}}_{k}\) is the set of all Republican, Democratic, and Libertarian candidates in the six offices in county k. We limited our validation to these three parties because affiliations for other choices can be reported in different ways by the county or voting machine, leading to mismatches even when the count is correct. For example, all our released counties (except for Santa Cruz, Arizona and Cumberland, New Jersey) include undervotes, but some counties do not report the number of undervotes in their official reports so we cannot verify all these numbers. We relied on MEDSL’s precinct data3 as our official vote count, and complemented it with official statements of the vote from counties directly where necessary.

We then release counties where the discrepancy is 1 percent or less. Figure 3 shows the distribution of discrepancies. In Panel 3a, we grouped the discrepancy rates in six categories, showing that 258 counties had no discrepancy across all six offices, and 104 had a candidate with non-zero discrepancies within 1 percent. Panel 3b shows the correlates of discrepancy by total votes cast. The discrepancies are dispersed across large and small jurisdictions. Panel 3c shows the distribution of candidate-level discrepancies, focusing on the range of −5 to 1 percent. We see that almost all the discrepancies are within 0.2 percent (and most are exactly zero). Some data points with 0 discrepancy are nevertheless not released and shown in light gray. This is because those counties have zero discrepancies in some offices but a discrepancy larger than 1 percent in other offices.

Fig. 3
figure 3

Discrepancy Rates. (a) number of counties by discrepancy. (b) relationship between discrepancy at the candidate level and total votes cast. (c) distriburion of discrepancies at the candidate level, limited to the neighborhood of -5 to 1 percent.

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In addition to computing discrepancies at the county-level, we also conducted a precinct-level validation. Our matching procedure described previously produced 23,139 precincts in 312 counties that could be matched to MEDSL’s standardized precinct names3. Figure 4 shows the alignment between the total votes for Presidential candidates in the CVR, per precinct, and the independently reported3 votes in the precinct we matched to. The match is not perfect due to the inclusion of counties with up to 1 percent discrepancies, and possible incorrect matches. Nevertheless, 20,139 precincts (out of 23,139 assigned) matched exactly, and 21,773 matched within 3 votes.

Fig. 4
figure 4

Precinct Level Validation. Comparisons of vote totals for each Presidential candidate at the precinct level, with those from a precinct-level database3 on the x-axis and those from our cast vote record database (with approximately matched precinct) on the y-axis. Axes are shown on a square root scale.

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Reasons for discrepancy

In the rare cases of discrepancies, we conducted an extensive, county-by-county investigation to reconcile the numbers, using state and county certification reports. Our public Github repository’s Issue feature documents our diagnosis for each problematic county that contains up-to-date diagnoses (https://github.com/kuriwaki/cvr_harvard-mit_scripts/issues). We found that the discrepancies tended to fall in one one of several categories.

First, in some counties, entire precincts were missing from the cast vote record data. This can happen if a county chooses to hand-count a batch of its ballots, or if the precinct’s ballots are processed differently.

Second, in some counties the cast vote record data did not include votes cast by certain methods (vote by mail, in-person, provisional). For example, in Santa Rosa County, Florida and Cuyahoga County, Ohio, it appears that the mailed-in votes have not been included in the cast vote record export uploaded to O’Donnell’s9 website. We verified this by comparing our counts with the county’s published vote totals broken out by vote method. This may occur if mailed and in-person votes are handled by a different tabulator.

Another type of known discrepancy is due to redactions done by counties to protect the integrity of the secret ballot, as we previewed in the Data Description section. Thirteen counties in Colorado and California provided CVRs where the vote choices of ballots in small ballot styles were removed. This practice is one way in which jurisdictions have tried to balance their dual roles of transparency and privacy. However, perfect redaction is known to be difficult because counties also need to report the total number of votes cast with perfect fidelity, and the redacted information can be backed out by triangulating the total election results. We do not attempt to unredact the CVRs.

There were many other counties with smaller discrepancies that could not be resolved with publicly available data. We believe one possible explanation for these minute discrepancies is the designation of provisional and disputed votes and ballot that were hand-tabulated. Our cast vote record may either exclude or include votes that were disputed but were later counted towards a major party candidate in the certified tally. For example, Dodge County, Wisconsin’s website cautions that

“Cast Vote Record (CVR) Reports are unofficial results from election night. These are the results the voting equipment tabulated on Election Day. The final, official canvass results posted on the Wisconsin Elections Commission’s website for any state/federal races also include counted provisional ballots and other small adjustments. These adjustments are not tallied by, or in, the voting equipment, [but] rather through the County Board of Canvass process. The Cast Vote Record (CVR) Reports contain all data fields available in the ES&S Election Software. Also, please note that if a Municipal Clerk has accidentally corrupted their election data after printing their results tapes and electronically transferring the results into the County for a specific election, that data will not be able to be archived and therefore, would have no ballots to be read and included in the CVR Report.” (https://bit.ly/46eISNX, accessed July 1, 2024).

While the dispute resolution process is publicly recorded on video in many counties, we cannot link each resolved ballot to a record in our database.

The case of Dane County, Wisconsin illustrates how several of these discrepancies can manifest. Figure 5 shows a precinct map of the county, which includes the City of Madison, using shapefiles4 with each precinct colored by the level of discrepancy compared to official reported results. Two precincts were missing from the Dane CVR because they were held by the neighboring county. Wisconsin cities and villages, which conduct their own election tabulation, may be located near a county border and straddle two counties. In three other instances, we found that a cast vote record from a town actually belonged to the jurisdiction of a different county. We learned that in two other precincts in Dane County, scanning machine failures prompted a hand-count of the votes, with no ballot image or cast vote record present. In 25 other precincts, the cast vote record was only 1 vote short of the reported election result. We contacted the Dane County clerk to resolve these issues, and obtained a letter written by the clerk’s office in 2021 that provided these explanations for the discrepancies42.

Fig. 5
figure 5

Reasons for Precinct Level Disrepancies. An example from each precinct in Dane County, Wisconsin.

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We chose to limit our inquiry to county clerks to a minimum, given that many are already at or above capacity in their day-to-day duties43. We believe it is unlikely that the original collectors of the data tampered with these remaining cases before posting because discrepancies are small and inconsequential for the apparent winner of the contest.

Usage Notes

In the remaining section, we illustrate how users can read in the data and analyze it. Although we use R as the running example, Python or any database-friendly programming language can read the dataset. We conclude with an example that studies the party loyalty of Republican and Democratic voters in their choice for President.

Reading in the data

We store our dataset in a parquet format. Parquet is a modern file storage format optimized for querying large datasets. It is partitioned by grouping variables, and it is columnar (so that users do not need to read in an entire row to extract a value from one column). Our dataset is prohibitively large to read and write in a plain-text format (20 Gb), but is compact and easy to read from in parquet (700 Mb). In R, we use the arrow package to query parquet files. For more information on how to read and write parquet files in R, see https://r4ds.hadley.nz/arrow. Parquet is also designed for usage in Python (https://arrow.apache.org/docs/python/parquet.html) and several other programming languages.

The following command opens the dataset.

library(tidyverse) library(arrow)

ds <‐ open_dataset("cvrs")

Here, "cvrs" indicates the path to the top-level folder containing the parquet files downloaded from Dataverse. Our data is organized by county, nested within states. After unzipping the zip file or by previewing on Dataverse, we see that cvrs has the following structure:

Because parquet is columnar, users will find it much faster to produce summary statistics of the data. Even though the code below counts some 166 million rows, it performs the count in one second on a personal laptop.

ds |> count(office) |> collect ()

## # A tibble: 6 × 2

## office

n

## <chr>

<int>

## 1 US PRESIDENT

42710448

## 2 US SENATE

19667514

## 3 US HOUSE

42613049

## 4 STATE SENATE

22146498

## 5 STATE HOUSE

38770601

## 6 GOVERNOR

562624

To perform this count, we used count() from dplyr (a package loaded via tidyverse), which totals the number of occurrences of each unique value in our office variable. We make use of R’s pipe operator, | > , to pass our data objects forward onto subsequent operations we want to perform. We then used the collect() command from arrow to extract the summary. All transformations before count() are lazily-loaded, meaning that they are not executed until needed. The arrow program combines the transformations internally in a way that avoids duplicative operations.

Application: Biden and Trump’s party loyalty

Here we ask whether partisans–defined by their votes for Congress and state legislature–vote for their party’s presidential candidate. Donald Trump was a polarizing candidate. Election observers have wondered if Trump drew less support from Republican-leaning voters compared to the support his opponent, Joe Biden, drew from Democratic-leaning voters. Some referred to these group of voters as Never Trump Republicans.

For this analysis, we study the counties in five battleground states which together decided the election: Wisconsin, Michigan, Georgia, Arizona, and Nevada. Biden won Georgia, Arizona, and Wisconsin by less than a percentage point, and won Nevada and Michigan by less than 3 percentage points.

ds_states <‐ ds |>

filter(state %in% c("WISCONSIN", "MICHIGAN", "GEORGIA", "ARIZONA", "NEVADA"))

Recall that aggregate election results report how many votes Biden and Trump received, but unlike cast vote records, they do not reveal which of those votes came from Republicans and Democratic voters. Only cast vote records can classify voters into partisan types based on how they voted in all offices except President.

We first need to narrow down our data so that we only use voter-contest pairs in contests contested by a Democrat and a Republican. In other words, the voter needed to have a choice to vote for a Republican or Democrat.

ds_contested <‐ ds_states |> collect() |> # Contested contestsfilter(any(party == "REP") & any(party == "DEM"), .by = c(state, office, district)) |># Ballots with Presidential vote filter(any(office == "US PRESIDENT"), .by = c(state, county_name, cvr_id))

The first filter() command in this code limits to vote choices for contested offices. For each state-office-district combination, we examine if there are any Republican candidates and any Democrats. Contests that do not meet this criteria are dropped. We see here that users should use the combination of the variables state, office, and possibly district to identify contests. To identify a particular candidate, users should further use the variables party or candidate.

The second filter() command limits to ballots with a Presidential choice. This excludes fragmented ballots where the President and the rest of the ballot is separated. As shown in this command, users should work with the cvr_id variable to identify a particular set of ballots. As discussed in the dataset description section, this ID is a numeric variable that is defined within counties, which are in turn unique within states (Two different counties in different states can have the same county_name value). These numbers do not in any way indicate the time in which the ballot was cast, or the personal identity of the voter. For more examples on how to extract such summaries from our data, see Supplementary Information E.

Both commands are done after collect() because the arrow package does not support group-specific filter commands as of version 16.1.0.

We now construct a dataset where each row is a single voter. We first create a dataset of Presidential votes:

## Voters based on President ds_pres <‐ ds_contested |> filter(office == "US PRESIDENT") |> select( state, county_name, cvr_id, candidate, pres_party = party) |> mutate(pres = case_when( pres_party == "REP" ~ "Trump", pres_party == "DEM" ~ "Biden", pres_party == "LBT" ~ "Libertarian", candidate == "UNDERVOTE" ~ "Undervote", .default = "Other"))

Separately, we construct a dataset that classifies the same voters based on their non-Presidential vote choice. The variable nonpres_party is Down-ballot Democrat if the voter only votes for Democrats down-ballot (using the all() command) and it is Down-ballot Republican if the voter only votes for Republicans down-ballot.

## subset to all‐Dem voters based on everything except Presidentds_D <‐ ds_contested |> filter(office != "US PRESIDENT") |> filter(all(party == "DEM"), .by = c(state, county_name, cvr_id)) |> distinct(state, county_name, cvr_id) |> mutate(nonpres_party = "Down‐ballot Democrat") ## same subset, but for all‐Rep voters ds_R <‐ ds_contested |> filter(office != "US PRESIDENT") |> filter(all(party == "REP"), .by = c(state, county_name, cvr_id)) |> distinct(state, county_name, cvr_id) |> mutate(nonpres_party = "Down‐ballot Republican")

Now we join voter’s choices for President with their down-ballot choices. Because each row is now a single voter, we join one-to-one using state, county_name, and cvr_id. Voters who were not classified into Democrats or Republican, are, by construction, those who voted for some Democratic down-ballot candidates and Republican down-ballot candidates, or undervoted in some of these offices. We label them Mixed voters.

ds_DR <- bind_rows(ds_D, ds_R) ds_analysis <‐ ds_pres |> left_join(ds_DR, by = c("state", "county_name", "cvr_id"), relationship = "one‐to‐one") |> mutate(nonpres_party = replace_na(nonpres_party, "Mixed"))

Finally, we construct a cross-tabulation of this dataset using the base-R xtabs() function.

xtabs(~nonpres_party + pres, ds_analysis) |>

addmargins()

##

pres

## nonpres_party

Biden Libertarian

Other

Trump Undervote

Sum

## Down-ballot Democrat

3430497

15087

12012

43239

4478

3505313

## Down-ballot Republican

70136

26723

12396

3540120

9166

3658541

## Mixed

793905

71431

21379

619255

16688

1522658

## Sum

4294538

113241

45787

4202614

30332

8686512

This table shows for example that among 3,505,313 solidly Democratic voters, 3,430,497 voted for Joe Biden. We can show cell counts in terms of proportions of the entire row, with the following base-R operation:

xtprop <‐ xtabs(~nonpres_party + pres, ds_analysis) |> prop.table(margin = 1) |> round(3) ## add margins N <- xtabs(~nonpres_party, ds_analysis) |> format(big.mark = ",") ## reorder columns and append totals xtprop[, c("Biden", "Trump", "Libertarian", "Undervote")] |> cbind(N) |> kableExtra::kbl(format = "latex", booktabs = TRUE)

This formatted table (Table 4) shows more clearly that the ticket splitting rate among solid partisans was on the order of 1 percent in this sample. Such small subgroups are almost impossible to detect in a survey. In contrast, 97 percent of solid Republicans stuck with their party’s nominee, Trump, and 98 percent of solid Democrats stuck with Biden. Trump’s party loyalty was a percentage point smaller than Biden’s.

Table 4 Party Loyalty in Five Battleground States. Each proportion shows the proportion of voters in each row group who voted for a particular Presidential candidate. N shows the number of voters in each group.
Full size table

A starker difference arises in the mixed group (those who vote for some Republicans and some Democrats, or undervoted, down-ballot). Biden won this group of weak partisans by more than 10 points. Close to 5 percent of this group voted for the third-party Libertarian candidate for President, instead of picking either Biden or Trump. Undervoting for President was low, around or less than 1 percent, across all groups.

More can be done to examine if these results vary by state, county, or precinct. Future versions of this dataset can also include ballot measures and local candidates that give more context for these patterns.