Elections: Statistical Analysis of Factors That Affected
Uncounted Votes in the 2000 Presidential Election (15-OCT-01,
GAO-02-122).
Following the 2000 presidential election, concerns were raised
about the election process, including the ability of some voting
equipment to render a complete and accurate vote count. Further,
minorities and disadvantaged voters were seen as more likely to
have their votes not counted because they may have used less
reliable voting equipment than affluent white voters. 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, there were statistically
significant effects on uncounted presidential votes. 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.
-------------------------Indexing Terms-------------------------
REPORTNUM: GAO-02-122
ACCNO: A02295
TITLE: Elections: Statistical Analysis of Factors That Affected
Uncounted Votes in the 2000 Presidential Election
DATE: 10/15/2001
SUBJECT: Elections
Electronic equipment
Voting records
Minorities
Disadvantaged persons
Standards and standardization
2000 Decennial Census
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GAO-02-122
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 equipment 1 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 correction 2 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 states 3 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 sample 4 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
Ballots cast Uncounted votes Voting 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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