Report to the Ranking Minority

Member, Committee on Government

Reform, House of Representatives

United States General Accounting Office

GAO

October 2001 ELECTIONS

Statistical Analysis of

Factors That Affected

Uncounted Votes in

the 2000 Presidential

Election

GAO-02-122
Page i GAO-02-122 Uncounted Presidential Votes

Letter 1

Scope and Methodology 2

Results in Brief 3

Background 4

Ballots Cast and Uncounted Presidential Votes Varied by Type of

Equipment 7

Voting Equipment Differed By Demographic Characteristics 7

Voting Equipment, Selected Demographic Characteristics, and

State Differences Affected Counties’ Percentages of Uncounted

Votes 8

Our Results Are Generally Consistent With Those of Other

Researchers 12

Appendix I Technical Approach and Additional Results 14

Our Database and Its Limitations 15

Regression Analysis: Approach and Results 17

Appendix II GAO Contacts and Staff Acknowledgments 21

GAO Contacts 21

Staff Acknowledgments 21

Tables

Table 1: Ballots Cast and Uncounted Presidential Votes by Type of

Voting Equipment 7

Table 2: Characteristics of Counties Used in GAO’s Analyses 8

Table 3. Coefficients of Various Regression Models Used to

Estimate the Percent of Uncounted Votes across Counties 17

Figure

Figure 1: Factors Accounting for Variation in Uncounted

Presidential Votes Across Counties 11

Contents
Page 1 GAO-02-122 Uncounted Presidential Votes

October 15, 2001

The Honorable Henry Waxman

Ranking Minority Member

Committee on Government Reform

House of Representatives

Dear Mr. Waxman:

Following the 2000 presidential election, a number of issues have been

raised concerning the election process, including the limitations of certain

types of voting equipment1

 in rendering a complete and accurate vote

count. Further, concerns have been raised about the possibility that

minorities and disadvantaged voters were more likely to have their votes

not counted because they may have cast their ballots using less reliable

voting equipment than affluent white voters. A limited body of prior

research exists that has studied these specific issues or a subset of these

issues in a comprehensive, systematic, and empirical manner.

You asked us to provide information on uncounted presidential votes in

the November 2000 general election and the extent to which these

uncounted votes could be attributed to counties’ voting equipment and

demographic characteristics. We further examined how much of the

difference in uncounted presidential votes across counties was related to

the state in which the counties are located, as well as the potential role of

error correction2

 in reducing uncounted votes due to voting errors.

Information on the reason votes for President were not counted was not

available, but may include voter error, equipment failure, election officials’

errors, or intentional nonvoting for the office of President.

 1

 For ease of presentation, we use the term “equipment” to refer to the five methods by

which votes were cast and counted in the 2000 presidential election. The five methods were

paper ballot, lever machine, punch card, optical scan, and electronic.

2

 Error correction refers to the ability of certain types of equipment to identify when a

voting error has occurred (e.g., if the voter cast a ballot that registered more than one vote

for the office of President). When error correction is used at the precinct level, voters are

notified that they have made an error on their ballot that would prevent their vote from

being counted and are given the opportunity to correct the error.

United States General Accounting Office

Washington, DC 20548
Page 2 GAO-02-122 Uncounted Presidential Votes

To address your request, we matched selected demographic data from the

U.S. Census Bureau with voting equipment, voter turnout, and presidential

vote data obtained from Election Data Services (EDS) and the Internet

web sites of state election officials. We statistically analyzed county-level

data to investigate relationships among counties’ demographic

characteristics, their voting equipment, and their percentages of

uncounted presidential votes. We also statistically controlled for the state

in which counties are located. We included data from 43 states3 and the

District of Columbia, representing 78 percent of the counties in the United

States. Our results should not be generalized beyond this set of locations.

The county demographic characteristics included from the 2000 Census

were population size, racial composition (percent of African American and

Hispanic residents in the county), and age (percent of 18-24 year olds and

residents over 65). We included estimates of median income and percent

of residents living below the poverty level from a 1997 Census model, and

education data (percent of high school graduates in a county) from the

1990 Census.

We measured uncounted presidential votes by subtracting the number of

votes for President from the number of total ballots cast. Both numbers

were included in EDS’ data along with voting equipment information for

each county. We supplemented the analysis using GAO survey data from a

representative sample4

 of county election officials to obtain further

information on the use of error correction in conjunction with the various

types of voting equipment.

Because of the unavailability of comprehensive data, we could not

determine why votes for President were not counted; could not distinguish

between ballots cast at the polling place on election day and those cast by

absentee ballot or through early voting; and could not assess the reliability

of different models of the same type of voting equipment. Additional

information on our methodology and its limitations is provided in

appendix I. We conducted our work from March through October 2001 in

accordance with generally accepted government auditing standards.

 3

 We excluded all voting jurisdictions in Alaska because they did not correspond directly to

election districts. Additionally, Arkansas, Maine, Mississippi, Missouri, Pennsylvania, and

Wisconsin were excluded because they did not report the necessary data to calculate

uncounted votes.

4

 The sample is a stratified random sample of election jurisdictions nationwide. See

Appendix I for more details.

Scope and

Methodology
Page 3 GAO-02-122 Uncounted Presidential Votes

While the state in which counties are located had more of an effect on the

number of uncounted presidential votes than counties’ demographic

characteristics or voting equipment, all three factors had statistically

significant effects on uncounted presidential votes.

The type of voting equipment that counties used in the 2000 general

election, for example, had an effect on uncounted presidential votes. The

largest percentages of uncounted presidential votes tended to occur in

counties that used punch card equipment. Counties that used optical scan

equipment with error correction had percentages of uncounted

presidential votes that were about 1.1 percentage points lower than

counties with punch card equipment. Potentially, an estimated 300,000

additional presidential votes may have been counted if counties that used

punch card equipment had, instead, used precinct-based optical scan

equipment with error correction. We did not have data available to assess

the extent to which other equipment changes, such as error correction

with punch card equipment, could have reduced the total number of

uncounted presidential votes.

Counties’ demographic characteristics also affected their percentages of

uncounted presidential votes. Specifically, counties with higher

percentages of minority residents tended to have higher percentages of

uncounted presidential votes, while counties with higher percentages of

younger and more educated residents tended to have lower percentages of

uncounted presidential votes. Counties that used punch card equipment

did not generally have higher percentages of minority, less educated, or

lower-income residents.

We found that the state in which counties are located had a greater effect

on counties’ percentage of uncounted presidential votes than did counties’

voting equipment and demographic characteristics combined. State

differences accounted for 26 percent of the total variation in uncounted

presidential votes across counties. State differences may have included

such factors as statewide voter education efforts, state standards for

determining what is a valid vote, the use of straight party ballots, the

number of candidates on the ballot, the use of provisional ballots, and the

extent to which absentee or early voting occurred. County demographic

characteristics accounted for 16 percent of the variation, and voting

equipment accounted for 2 percent of the variation. A supplemental

analysis of a subset of 404 counties showed that using optical scan

equipment with error correction accounted for an additional 4 percent of

the variation in counties’ uncounted presidential votes. The remaining 52

percent of the variation was due to unknown factors for which we had no

Results in Brief
Page 4 GAO-02-122 Uncounted Presidential Votes

data, such as whether a county switched to a new type of voting

equipment or the number of inexperienced voters in a county.

Each state and the District of Columbia play a role in elections by

establishing election laws, policies, and procedures. In most states,

counties are responsible for conducting elections, including selecting

countywide voting equipment, counting ballots, and reporting elections

results. In separate reports, we provide more in-depth information on

election issues relating to people, processes, and technology at the county

and state levels.5

The equipment on which votes were cast and counted in the November

2000 election can be placed into five categories: paper ballots, lever

machines, punch cards, optical scan, and electronic. Three of these five

types of equipment—lever, optical scan, and electronic—have some

capability or can be used to prevent or allow for the correction of voting

errors.

Paper ballots. Paper ballots list the names of the candidates and the issues

to be voted on. Voters generally complete their ballots in the privacy of a

voting booth, recording their choices by placing marks in boxes

corresponding to the candidates’ names and the issues. After making their

choices, voters drop the ballots into sealed ballot boxes. Election officials

gather the sealed boxes and transfer them to a central location, where the

ballots are manually counted and tabulated.

Lever machines. Lever machine “ballots” consist of a rectangular array of

levers. Printed strips listing the candidates and issues are placed next to

each lever. Voters cast their vote by pulling down the levers next to the

candidates or issues of their choice. After voting, the voter moves a

handle, which automatically records the vote and resets the levers. Votes

are tallied by mechanical counters, which are attached to each lever. At

the close of the election, election officials tally the votes by reading the

counting mechanism totals on each lever voting machine. A feature

inherent to lever machines is that they prevent voters from overvoting (i.e.,

voting more than once for the same office, unless the ballot explicitly

 5 Elections: Perspectives on Activities and Challenges Across the Nation (GAO-02-03, Oct.

15, 2001).

Background

Types of Equipment Used

in the November 2000

Election
Page 5 GAO-02-122 Uncounted Presidential Votes

allows for more than one choice to be made). Overvoting is prevented by

the interlocking of the appropriate mechanical levers in the machine.

Punch cards. Punch card voting equipment generally consists of a ballot, a

vote recording device, a privacy booth, and a computerized tabulation

device. Votes are cast by inserting the ballot into the vote recording device

and punching a hole through the ballot such that the hole corresponds to

the voter’s ballot choice. Votes cast on punch card equipment are machine

readable. Votes are tabulated using vote tabulation machines, and

software is used to program each vote tabulation machine to correctly

assign each vote read into the computer to the proper race and candidate

or issue. The two basic types of punch card devices are Votomatic and

Datavote.

Optical scan. An optical scan voting system is comprised of computerreadable ballots, appropriate marking devices, privacy booths, and a

computerized tabulation machine. The ballot lists the names of the

candidates and the issues. Voters record their choices using an

appropriate writing instrument to fill in boxes or ovals, or to complete an

arrow next to the candidate’s name or the issue. Like punch card software,

the software for optical scan equipment is used to program the tabulation

equipment to correctly assign each vote read into the computer to the

proper race and candidate or issue. Optical scan equipment based in

precincts can be programmed to detect and reject both overvoting and

undervoting (i.e., not registering a vote for every race and/or issue on the

ballot). Using such error correction technology could allow voters to fix

their mistakes before leaving the polling place. If ballots are tabulated

centrally, voters do not have the opportunity to correct mistakes that may

have been made.

Electronic. Electronic equipment (also called Direct Recording Electronic

or DRE) comes in two basic types, pushbutton or touchscreen, with the

pushbutton being the older and more widely used of the two. For

pushbuttons, voters press a button next to the name of the candidate or

the issue, which then lights up to indicate the selection. Similarly, voters

using touchscreens make their selections by touching the screen next to

the candidate or issue, which is then highlighted. When voters are finished

making their selections, they cast their votes by pressing a final “vote”

button or screen. Because all electronic equipment is programmable, it

does not allow overvotes. In addition, voters can change their selections

before hitting the final button to cast their votes.
Page 6 GAO-02-122 Uncounted Presidential Votes

There have been several broad-based studies that have examined

relationships among voter demographics, voting equipment, and/or

uncounted votes. These studies, whose methods and findings we did not

independently verify, included the following.

• A recent research study estimated that about 1.5 million voters thought

they had voted for President but did not have their votes for President

counted in the 2000 election. Faulty voting equipment and confusing

ballots were among the stated reasons for the ballots being unmarked,

spoiled, or too ambiguous to count. The study reported that punch card

and electronic voting equipment were associated with uncounted votes for

President exceeding 2 percent of all ballots cast. (CalTech/MIT, July 2001.)

• Another recent research study reported that, despite the perception that

minorities and poor people were disproportionately more likely to vote on

antiquated voting machinery and therefore have their ballots invalidated,

the data did not support this contention. The study found that in the

majority of states, whites and non-poor voters were more likely than

African Americans and poor voters to reside in counties that used punch

card equipment, based on 1998 voter equipment data. (Knack & Kropf, Jan.

2001.)

• A study of invalidated ballots in the 1996 presidential election found that

counties with more African Americans and Hispanics were more likely to

have higher rates of invalidated ballots, particularly in counties using

punch card machines, optical scanners with centralized (as opposed to

precinct-based) counting, and hand-counted paper ballots. When counties

used equipment that can be programmed to prevent overvoting (i.e., lever

technology, electronic voting technology, and precinct-count optical scan

systems), racial differences in the rate of invalidated votes disappeared.

(Knack & Kropf, May 2001.)

• A study of the 2000 presidential election found that the percentage of

uncounted votes in 20 congressional districts with low-income/highminority populations were higher, regardless of the type of voting

equipment used, than in 20 congressional districts with high-income/lowminority populations. In both types of districts, the percent of uncounted

votes was highest when punch card equipment was used. (House

Committee on Government Reform, Minority Staff, Special Investigations

Division, July 2001)

Other Studies of

Uncounted Votes
Page 7 GAO-02-122 Uncounted Presidential Votes

In the November 2000 presidential election, there were over 85 million

votes cast in the 2,455 counties in our analysis and, of those, 1.6 million

votes for President were not counted. The percentage of uncounted votes

ranged from 0 percent to 23 percent, with an average of 2.3 percent. Only

12 counties had percentages of uncounted votes that exceeded 10 percent.

Of the 2,455 counties, 284 (or 12 percent) used electronic voting

equipment, 381 (16 percent) used lever equipment, 1,095 (45 percent) used

optical scan equipment, 213 (9 percent) used paper ballots, and 482 (20

percent) used punch card equipment.6

 Furthermore, Table 1 shows that

while 35 percent of the ballots cast came from counties using punch card

equipment, 49 percent of the uncounted presidential votes were cast on

punch card equipment.

Table 1: Ballots Cast and Uncounted Presidential Votes by Type of Voting

Equipment

Voting Ballots cast Uncounted votes

equipment Number Percent Number Percent

Electronic 11,604,770 14 184,132 11

Lever machines 13,557,499 16 255,196 16

Optical scan 29,338,967 34 386,011 23

Paper ballots 634,407 1 12,010 1

Punch card 30,195,730 35 805,635 49

Total 85,331,373 100 1,642,984 100

Source: GAO analysis of EDS data.

Counties with different voting equipment differed demographically. (See

table 2.) Counties that used punch cards, for example, had larger

populations; higher median incomes; and smaller percentages of residents

over 65 years of age and persons living below the poverty level than

counties using other types of voting equipment. Our analysis did not show

that minorities, or persons with less education or income, were more

likely than others to be found in counties that used punch card voting

equipment, the equipment associated with higher percentages of

uncounted presidential votes. As the final row of table 2 shows, before

controlling for demographic characteristics or state differences, the

average percent of uncounted presidential votes was higher in counties

 6

 The sum of the percentages of types of voting equipment does not equal 100 percent due

to rounding.

Ballots Cast and

Uncounted

Presidential Votes

Varied by Type of

Equipment

Voting Equipment

Differed By

Demographic

Characteristics
Page 8 GAO-02-122 Uncounted Presidential Votes

that used punch cards (2.9 percent) than in other counties (2.1 percent to

2.3 percent).

Table 2: Characteristics of Counties Used in GAO’s Analyses

Voting equipment used

Averages for County

Characteristics

Punch

card

(482)

Electronic

(284)

Lever

machine

(381)

Optical

scan

(1,095)

Paper

ballots

(213)

Population 172,612 108,913 96,389 70,464 6,382

Percent African American 6.3 10.8 17.8 7.6 1.3

Percent Hispanic 6.5 6.1 3.3 7.6 3.0

Percent high school graduates 46.3 41.7 40.4 45.7 48.6

Percent 18 to 24 years old 9.3 9.2 9.5 8.9 6.6

Percent over 65 years of age 13.9 13.4 13.8 15.0 18.5

Percent below poverty level 13.1 16.1 16.9 14.8 14.5

Median income 35,513 32,692 31,587 33,066 28,963

Percent uncounted votes 2.9 2.3 2.2 2.1 2.3

Note: Numbers of counties for which we had complete data on voting equipment, uncounted

presidential votes, and demographic characteristics are given in parentheses. Counties with mixed

equipment were not used in our analysis.

Source: GAO’s analysis of EDS’ and the Census Bureau’s data.

Overall, while we found that counties’ percentages of uncounted

presidential votes were related to their voting equipment and demographic

characteristics, these factors accounted for less of the variation in

uncounted votes across counties than did the state in which the county is

located.

To determine how the percentages of uncounted votes across the counties

for which we had data were affected by voting equipment, demographic

characteristics, and the state in which counties are located, we used

robust regression models that adjusted for the clustering (i.e., the lack of

independence) of observations within states. Our statistical model

included type of voting equipment, county demographic variables, and a

set of variables to control for differences across states in which counties

are located. (See app. I, table 3 for a more detailed discussion of all models

and effects.)

Voting Equipment,

Selected

Demographic

Characteristics, and

State Differences

Affected Counties’

Percentages of

Uncounted Votes
Page 9 GAO-02-122 Uncounted Presidential Votes

Our statistical model indicated that there were no significant differences in

uncounted presidential votes among counties that use electronic, paper,

and optical scan voting equipment. Counties with punch cards had

percentages of uncounted presidential votes that were roughly 0.6

percentage points higher than those counties, and counties with lever

machines had percentages of uncounted presidential votes that were 0.7

percentage points lower than those counties. Given that the average of the

uncounted presidential votes across all counties was roughly 2 percent,

these represent sizable, as well as statistically significant, differences.

When the same statistical model was run for the subset of 404 counties

that we surveyed, we found an additional equipment effect. The survey

asked county election officials if they used equipment that either

prevented errors or identified errors for voters so the ballot might be

corrected. Since both electronic and lever equipment prevent overvotes,

almost all of the counties using those types of equipment reported using

error correction. In addition, almost all of the counties using punch card

equipment and paper ballots reported not having or using error correction

capabilities. Therefore, responses to the survey allowed us to distinguish

between counties with optical scan equipment that used error correction

and those that did not use it. Doing so resulted in significant differences

between types of equipment. Counties using punch cards had uncounted

presidential votes that were 1.1 percentage points higher than counties

using error-corrected optical scan equipment. If we apply these results to

the larger set of 2,455 counties, an estimated 300,000 additional votes may

have been counted if counties that used punch card equipment had,

instead, used precinct-based optical scan equipment with error correction.

After we statistically controlled for the effects of state differences and

voting equipment, uncounted presidential votes in our dataset of 2,455

counties were significantly higher in counties with higher percentages of

African Americans and Hispanics. Each percentage point increase in a

county’s population of African Americans was associated with a 0.02

percentage point increase in the county’s uncounted presidential votes.

Each percentage point increase in a county’s population of Hispanics was

associated with a 0.01 increase in the county’s uncounted presidential

votes. This means, for example, that we would expect that a county where

African Americans made up 35 percent of the population would have had

uncounted presidential votes that were 0.6 percentage points higher than a

county where African Americans made up 5 percent of the population.

Counties That Used Punch

Card Equipment Had

Higher Percentages of

Uncounted Presidential

Votes

Race, Education, and Age

Affected Uncounted

Presidential Votes
Page 10 GAO-02-122 Uncounted Presidential Votes

After we statistically controlled for the effects of state differences and

voting equipment, uncounted presidential votes in our dataset of 2,455

counties were significantly lower in counties with higher percentages of

high school graduates and 18- to 24 year-olds. Each percentage point

increase in a county’s population of high school graduates was associated

with a 0.06 percentage point decrease in the county’s uncounted

presidential votes. Likewise, each percentage point increase in a county’s

population of 18- to 24-year-olds was associated with a 0.03 percentage

point decrease in the county’s uncounted presidential votes. This means,

for example, that we would expect that a county where high school

graduates made up 50 percent of the population would have had

uncounted presidential votes that were 1.8 percentage points lower than a

county where high school graduates made up 20 percent of the population.

We next determined the incremental effects of voting equipment, county

demographics, and state differences on counties’ percentage of uncounted

presidential votes. When we just included type of equipment in the

statistical model, we found that equipment alone explained 2 percent of

the variation in uncounted presidential votes across counties. When we

added demographic variables to that model, the county demographics

explained an additional 16 percent of the variation. Next, we included a set

of variables to statistically control for differences across the states in

which counties are located. This made it possible to account for an

additional 26 percent of the variation in uncounted presidential votes. A

supplemental analysis of a subset of 404 counties that we surveyed

showed that including a county’s use of error correction with optical scan

equipment would explain an additional 4 percent of the variation in

uncounted votes across counties.

State Differences

Accounted for More

Variation in Uncounted

Presidential Votes Than

Voting Equipment and

Demographic Variables

Combined
Page 11 GAO-02-122 Uncounted Presidential Votes

Figure 1: Factors Accounting for Variation in Uncounted Presidential Votes Across

Counties

Source: GAO’s analysis of EDS’ data, the Census Bureau’s data, and GAO’s survey data.

Differences across states were of considerable importance in determining

the prevalence of uncounted presidential votes and accounted for more of

the variability (26 percent) in uncounted presidential votes across counties

than demographic characteristics and type of voting equipment used

combined. The following factors, for which we had no data because they

have not been measured in a comprehensive, systematic way, are among

those that may have contributed to differences among states: (1) voter

education efforts, such as making sample ballots available prior to election

day; (2) the use of straight party ballots that enable voters to make one

entry to cast votes for all offices on the ballot; (3) the number of

candidates on the ballot (including presidential, gubernatorial, or

congressional candidates); (4) the number of provisional ballots cast,7

 and

percentage of provisional ballots that were not counted; and (5) the extent

to which absentee and/or early voting occurred and if such ballots were

counted using a different voting equipment than ballots cast on election

day.

The remaining 52 percent of the variation was due to unknown factors for

which we had no data, such as whether a county switched to a new type of

voting equipment or the number of inexperienced voters in a county.

 7

 Provisional ballots are ballots that are cast by voters who may not be properly registered

when they arrive at the polling place. After election day, their situation is reviewed and

election officials make a decision as to whether the vote should be counted or not.

52% 26%

16%

Unknown

State differences

County demographics

overall

Voting equipment 2%

Error correction 4%a
Page 12 GAO-02-122 Uncounted Presidential Votes

Like all four of the studies cited earlier in this report, we found that punch

card equipment was associated with higher percentages of uncounted

votes in counties, although our findings did not indicate, as did those of

CalTech/MIT, that electronic voting equipment was similarly problematic.

We also found, like Knack and Kropf, that minorities and persons with

lower income were not more likely than others to reside in counties that

used punch cards, and that counties with higher percentages of African

Americans had higher percentages of uncounted presidential votes. We did

not find, however, that the racial difference “disappears” in counties with

certain voting equipment. Also, while there were differences between our

study and that of the Special Investigation (e.g., our analytic methods did

not involve making the same specific comparisons, and we analyzed

counties while they analyzed congressional districts, our results do

indicate, like theirs, that regardless of voting equipment, percentages of

uncounted presidential votes were higher in high minority areas than in

other areas.

To the extent that our results are not consistent with the findings of

others, factors that may account for these differences include the variables

included in the analyses, the number of counties included in the dataset,

and the age of the data used by the different studies.

This report is one of several GAO studies addressing election issues. Our

other reports discuss in greater depth election issues such as the scope of

congressional authority in election administration, voter registration,

absentee and early voting, voting assistance for military and overseas

voters, election day administration, voting accessibility for voters with

disabilities, vote counts and certification, Internet voting, and voting

equipment standards.

Our Results Are

Generally Consistent

With Those of Other

Researchers
Page 13 GAO-02-122 Uncounted Presidential Votes

We are sending copies of this report to the Chairman of your Committee

and to other congressional committees. Staff members who contributed to

this review are acknowledged in appendix II. If you or your staff have any

questions about this report, please contact me on (202) 512-8777.

Sincerely yours,

Laurie E. Ekstrand

Director, Justice Issues
Appendix I: Technical Approach and

Additional Results

Page 14 GAO-02-122 Uncounted Presidential Votes

This appendix provides information on our analyses of uncounted

presidential votes in the November 2000 general election and the extent to

which these uncounted votes were affected by counties’ voting equipment,

demographic characteristics, and state differences. It also discusses a

separate analysis of a subset of counties in which we explored the

potential of using optical scan equipment with error correction capability

to reduce uncounted votes.

To obtain this information, we purchased data on equipment used in and

results of the November 2000 election from Election Data Services (EDS),

a company that compiles data on election administration and election

results from the election jurisdictions of each state. Using EDS’ election

results data, we could calculate the number of uncounted presidential

votes by subtracting the number of votes for President from the number of

total ballots cast.

For the most part, EDS’ data files for the 2000 presidential election are

county level tabulations of election returns, voter participation, election

official contact information, and voting equipment information. For

Alaska, data are provided for election districts and regions, rather than

counties; for the New England states, additional data are included for

cities and townships within counties.

We matched data from the U.S. Census Bureau on selected demographic

characteristics of each county with data on voting equipment and election

results from EDS. From the 2000 Census, we included the following

demographic variables in our analyses: population size, racial composition

(percent African American and percent Hispanic), and age (percent 18 to

24 and over 65). From a 1997 Census model, we used estimates of median

income and percent of residents living below the poverty level. Because

more current data were not available, we used education (percent high

school graduates) from the 1990 Census. We selected these demographic

variables to include in our analysis because they have been included in

prior studies of uncounted votes.

We also analyzed data for a subset of 404 counties whose election officials

were surveyed by GAO in May 2001. The sample frame consisted of (1) all

county election jurisdictions, or their equivalents, in 39 states that delegate

election responsibilities primarily to counties; (2) the largest minor civil

division in each county in the nine states that delegate election

responsibilities to minor civil divisions; (3) the District of Columbia; and

(4) Alaska. The sample was a stratified random sample of 607 election

Appendix I: Technical Approach and

Additional Results

Data Sources
Appendix I: Technical Approach and

Additional Results

Page 15 GAO-02-122 Uncounted Presidential Votes

jurisdictions nationwide selected from three strata—jurisdictions that

used electronic voting equipment; those that used optical scan; and those

that used any other method, including punch cards, lever machines, and

hand-counted paper ballots. Of the 607 questionnaires sent, 513 usable

questionnaires were returned. In our analyses of the questionnaire data,

we included responses from the 404 counties and excluded responses

from minor civil divisions to remain consistent with the unit of analysis in

our larger county level analysis. One question in the survey asked: “Did the

voting equipment used for votes cast at precincts on Election Day for the

November 2000 general election either prevent errors or identify errors for

voters so they could correct their ballots at the polling place?” From the

responses to this question, we were able to distinguish, for these 404

counties, those using optical scan equipment with error correction and

without.

We verified EDS’ voting equipment data using several sources.

Specifically, we (1) checked the Internet sites of 10 secretaries of state, (2)

reviewed 2 state reports that provided information on the voting

equipment used by counties and/or minor civil divisions, and (3) reviewed

responses to a nationwide mail survey of election jurisdictions for other

elections work GAO undertook. We made corrections where necessary.

To verify and augment election results data EDS provided us, we checked

the Internet sites of secretaries of state and spoke with several state and

county election officials. As result of these efforts, we verified a

substantial portion of EDS’ election results data and added 230 counties in

4 states (Delaware, Oklahoma, Tennessee, and West Virginia) and 147

counties in Texas to our database.

Based on the extent and nature of our data verification, we are confident

that the data used in our analyses are of sufficient quality to support our

conclusions.

Our database consisted of demographic, voting equipment and election

results data for each of 2,455 counties in 43 states and the District of

Columbia. The database included 78 percent of the nation’s 3,141 counties

at the time of the 2000 presidential election. To our knowledge, these data

were the most recent, comprehensive, and valid data available to address

the research questions specified for our study. Notwithstanding the

strengths of our database, the precision of our analytic results and our

Data Quality

Our Database and Its

Limitations
Appendix I: Technical Approach and

Additional Results

Page 16 GAO-02-122 Uncounted Presidential Votes

ability to explain why they occurred are limited by a number of factors,

including missing data, omitted variables, and measurement error.

For several reasons, we did not include a number of states and counties in

our database. Specifically, we excluded (1) all counties in 6 states

(Arkansas, Maine, Mississippi, Missouri, Pennsylvania, and Wisconsin),

107 counties in Texas, 1 county in Alabama and 1 county in Oklahoma

because these counties did not report the necessary data to calculate

uncounted votes; (2) all voting jurisdictions in Alaska because they did not

correspond directly to election districts; (3) counties that used a mix of

voting equipment; (4) counties in which the reported numbers of votes

cast for President exceeded the number of persons who turned out to

vote; and (5) 1 county in which it appeared that only half the persons who

turned out to vote cast a vote for President.

Our results should be interpreted with caution for the following reasons:

(1) The available data did not distinguish between votes cast at the polling

place on election day and those cast by absentee ballot or through early

voting. Because some locations used different equipment for absentee

and/or early voting, we could not assess the impact of such differences on

our results. (2) We did not have information on the particular model of

voting equipment used, so uncounted presidential votes, even within a

single county, may have been affected by differences in the reliability of

different models of the same equipment. (3) We used aggregate countylevel demographic data as a proxy for the characteristics of voters because

we did not have data on individual voters. (4) We could not determine why

votes for President were not counted. For example, we could not discern

if uncounted presidential votes were due to voter error, equipment failure,

errors on the part of election officials, or intentional nonvoting for the

office of President.1

 (5) In the absence of more current data, we analyzed

1990 Census data on education, which may have had different

relationships with other variables in 2000 than it did in 1990. The extent to

which such relationships may have changed is unknown. (6) Because our

data on income and poverty were estimates derived from statistical

models, they contained an unknown amount of measurement error that

could not be accounted for in our statistical models.

 1

 Research by others has indicated that the percentage of voters who reported deliberately

not voting for President in the 2000 election was small (0.34 percent).
Appendix I: Technical Approach and

Additional Results

Page 17 GAO-02-122 Uncounted Presidential Votes

Our analyses included, along with descriptive statistics, analysis of

variance methods and robust regression models that account for the

clustering.

To determine how the percentage of uncounted presidential votes was

affected by the voting equipment employed in and the demographic

characteristics of the counties for which we had data, we used a series of

four robust regression models that adjusted for the clustering (i.e., the lack

of independence) of observations within states. Model 1 in table 3

indicates that when demographic and other differences across counties

are ignored, the average percentage of uncounted votes was significantly

higher in counties that used punch card equipment than in counties that

used optical scan equipment (which is the deleted referent category).

Counties that used electronic, paper, or lever equipment, on the other

hand, were not significantly different from those that used optical scan

equipment. The R-squared value (i.e., the value representing the

proportion of variation that the statistical model explained) for Model 1

indicates that differences in voting equipment accounted for only 2

percent of the variation in the percentage of uncounted votes across

counties. This effect of voting equipment on uncounted votes may be due

to various differences between types of equipment such as the design of

the equipment by the manufacturer, the operation of the equipment by

voters, or the processes that election officials used to prepare and operate

the equipment.

Table 3. Coefficients of Various Regression Models Used to Estimate the Percent of

Uncounted Votes across Counties

Characteristic Model 1 Model 2 Model 3 Model 4

Intercept 2.07 5.59 6.03 3.39

Punch card 0.80** 1.08** 0.63**

Electronic 0.20 0.11 -0.32

Lever 0.10 -0.36 -0.72**

Paper 0.19 -0.10 -0.35

Population (logged) -0.20** -0.27** -0.13

Percent African American 0.03* 0.03** 0.02**

Percent Hispanic 0.00 0.00 0.01*

Percent high school graduates -0.03 -0.04 -0.06**

Percent 18 to 24 years old -0.02 -0.02 -0.03**

Percent over 65 years old 0.01 0.02 0.04

Percent below poverty level 0.00 0.01 0.02

Median income (in 1000s) 0.00 0.00 0.00

R- squared 0.02 0.12 0.18 0.44

Regression Analysis:

Approach and Results
Appendix I: Technical Approach and

Additional Results

Page 18 GAO-02-122 Uncounted Presidential Votes

Notes: All models are robust regression models that account for clustering, and the lack of

independence of observations, within states. Model 4 differs from Model 3 by including a set of 42

dummy variables to allow for effects of unmeasured state characteristics. We have omitted the

coefficients associated with the dummy variables to simplify our presentation.

* Statistically significant at the 0.05 confidence level.

** Statistically significant at the 0.01 confidence level.

Source: GAO’s analysis of EDS’ and the Census Bureau’s data.

When assessing the effects of demographic characteristics while ignoring

differences in voting equipment across counties, as in Model 2, we found

that the percentage of uncounted presidential votes was significantly

higher in counties with smaller populations and in counties with higher

percentages of African Americans. Other factors were not statistically

significant. The demographic measures we considered, taken together,

accounted for about 12 percent of the variability in the percentage of

uncounted votes across counties. When we considered voting equipment

and demographic factors jointly in Model 3, (1) we were able to account

for 18 percent of the variation across counties in the percentage of

uncounted presidential votes, and (2) punch card equipment, population

size, and percent African American remained statistically significant. That

is, regardless of county demographics, counties that used punch card

equipment had higher percentages of uncounted presidential votes.

Additionally, regardless of voting equipment, counties with higher

percentages of African Americans had higher percentages of uncounted

votes, and counties with larger populations had lower percentages of

uncounted presidential votes.

In our final model, Model 4, we estimated these same effects after allowing

not only for clustering but also for differences across counties that were

due to the unmeasured effects of the states they are located in. Using

dummy variables (the coefficients for which are deleted from table 3) to

allow these effects made it possible to account for about 44 percent of the

variation in uncounted presidential votes. Moreover, Model 4 indicates

that once this full set of differences was accounted for, there were no

differences in uncounted presidential votes among counties that use

electronic, paper, or optical scan voting equipment. Counties with punch

cards had roughly 0.6 percentage points higher percentages of uncounted

presidential votes than those counties, and counties with lever equipment

had 0.7 percentage points lower percentages of uncounted presidential

votes than those counties. Given that the average uncounted votes across

all counties was roughly 2 percent, these represent sizable, as well as

statistically significant, differences.
Appendix I: Technical Approach and

Additional Results

Page 19 GAO-02-122 Uncounted Presidential Votes

The only demographic variables that were associated with significantly

higher percentages of uncounted presidential votes when the state and

voting equipment effects were controlled, were higher percentages of

residents who were African American and Hispanic. The demographic

variables that were associated with significantly lower percentages of

uncounted presidential votes when the state and voting equipment effects

were controlled included higher percentages of high school graduates and

18 to 24 year-olds in the county. Characteristics of voters did not appear to

interact with voting equipment to affect the percentage of uncounted

votes, although our aggregated data were not well suited to addressing this

issue. Models that included interactions between voting equipment and

demographic characteristics (not shown) accounted for only about 1

percent of the variation in uncounted votes across counties.

An additional key finding of our study was that differences across states

were of considerable importance in determining the prevalence of

uncounted presidential votes and accounted for more of the variability

across counties in uncounted presidential votes (26 percent) than

demographic characteristics (16 percent) and type of voting equipment (2

percent) combined. The following factors for which we had no data are

among those that may have contributed to differences among states:

1. voter education efforts, such as making sample ballots available prior

to election day;

2. the use of straight party ballots that enable voters to make one entry to

cast votes for all offices on the ballot;

3. the number of candidates on the ballot (including presidential,

gubernatorial, or congressional candidates);

4. the number of provisional ballots cast, and percentage of provisional

ballots that were not counted; and

5. the extent to which absentee and/or early voting occurred and if such

ballots were counted using a different voting equipment than ballots

cast on election day.

When we ran Model 4 for a subset of 404 counties that GAO surveyed, we

found an additional equipment effect. This survey asked county election

officials if they used equipment that either prevents errors or identifies

errors for voters so the ballot might be corrected. Since both electronic

and lever equipment prevent “overvotes,” almost all of the counties using
Appendix I: Technical Approach and

Additional Results

Page 20 GAO-02-122 Uncounted Presidential Votes

those types of equipment reported using error correction. In addition,

almost all of the counties using punchcard equipment and paper ballots

reported not having or using error correction capabilities. Therefore,

responses to the survey allowed us to distinguish between counties with

optical scan equipment that used error correction and those that did not

use it. Doing so resulted in significant differences between types of

equipment. Counties using punch cards had significantly higher

percentages of uncounted presidential votes than counties using error

corrected optical scan equipment by 1.1 percentage points. If the

relationship that we found in these 404 counties holds true for the larger

set of 2,455 counties, an estimated 300,000 additional votes may have been

counted if counties that used punch card equipment had, instead, used

precinct-based optical scan equipment with error correction.
Appendix II: GAO Contacts and Staff

Acknowledgments

Page 21 GAO-02-122 Uncounted Presidential Votes

Laurie E. Ekstrand (202) 512-8777

Evi L. Rezmovic (202) 512-8777

In addition to the above, Wendy Ahmed, Douglas Sloane, David Alexander,

Amy Lyon, and Tanya Cruz made key contributions to this report.

Appendix II: GAO Contacts and Staff

Acknowledgments

GAO Contacts

Staff

Acknowledgments

(440052)

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