Man vs. Voting Machine: The
2000
by
Dale Bremmer
Professor of Economics
HSS Department
Rose-Hulman Institute of
Technology
and
Randy Kesselring
Professor of Economics
Department of Economics and
Decision Sciences
June 2003
Man vs. Voting Machine: The 2000
I. Introduction
After
the 2000 presidential election in
It
was alleged that voting officials intentionally used antiquated voting machines
in counties with larger populations of low-income families, minorities, and
senior citizens on fixed incomes. The
argument is that these traditionally Democrat constituents would have greater
difficulty using the older voting technology, would be more likely to commit
mistakes during voting, and, consequently, would spoil more of their
ballots. As a result, more of their
ballots would be thrown out, leading to a Republican majority.[1]
Others
contend that Democratic county officials and election boards controlled by a
Democratic majority intentionally used older technology knowing that a large
percent of their traditional supporters would spoil their ballots and diminish
their party’s margin. A Newsweek
columnist wrote that the poor ballot design and voting instructions given by
the Democratic officials in
This
paper attempts to quantify the socio-economic factors that affected the
selection of the voting machines used in each of
Investigating
whether the choice of the voting technology affected the election outcome,
simple regression analysis suggests that the use of punch-card machines did not
affect the number of Democratic, Republican, or Reform party votes. There is positive, but weak, correlation
between use of punch-card machines and votes for the Green party.
Another
interesting question is the impact of punch-card machines on the residual vote
- - the difference between the voter turnout in the county and the number of
votes for president. The Cal Tech - MIT
Voting Technology Project estimates that, for the whole of
However,
while ordinary least squares fails to find a statistically significant
relationship between the choice of voting machines and election outcomes,
sample selection econometric techniques yield different results. These results indicate an endogenous
relationship between the voting technology selected and the votes cast. Contrary to the allegations of selecting
voting machines biased against Democratic votes, a “structural” equation shows
that counties with a higher expected level of Democratic votes were less likely
to select the punch-card technology.
Following
this introduction, the second section of the paper reviews the voting technology
used in the
II. Voting Machines in the
Since
their inception in the state of
Table
1 lists the various type of voting technology used in the
As
shown in Table 2, during the 2000 presidential election there were no
electronic voting machines in
Given
the cost of new voting technology and limited state and county budgets, doing
away with the older technology and adopting new technology is problematic. Less than twelve companies make voting
machines, and few of these firms have excess capacity. Voting officials and executives of the voting
equipment industry have estimated that it could take a decade to upgrade
punch-card voting machines to the newer optical-scan or electronic
technologies.[4] The number of trained employees is limited,
which further restricts the adoption of new technology. Also, the preferences of voters and officials
of state and county election boards would affect the time necessary to accomplish
such a changeover.
As
witnessed by the recent 2002 primary in
III. Literature Review:
Econometric Studies of Elections
The
econometric analysis of
Econometric Analysis of National Elections
When analyzing the outcome of U.S.
presidential elections on the national level, the popular dependent variable
used in econometric models is the percentage of the votes received by one of
the two major political parties - - Republican or Democrat.[7] The explanatory variables include economic
variables, measures of incumbency, and other measures of the incumbent party’s
political strength. Independent
variables that measure the performance of the economy have included the growth
in real GDP per capita and the inflation rate.
The party of the incumbent has been denoted by dummy variables. Some papers have included a “duration”
variable that measures how long a political party has controlled the White
House. The underlying hypothesis is that
the advantage of being an incumbent is reduced the longer a party is in power. Studies using state-level data generally
include a binary variable to indicate whether the presidential and
vice-presidential candidate was a “favorite son” from a given state.
Other
studies have used variables to capture national security concerns. Proxy variables used for this purpose include
changes in the proportion of the population serving in the armed forces. Other variables have been included to measure
race and other social concerns. The
approval rating of the incumbent president has been included as an explanatory
variable as has other measures of presidential popularity.
Finally,
other explanatory variables have included the percentage of votes a given party
garnered in the primary election. The
number of seats in the House of Representatives that the incumbent party lost
in the previous election two years previous has been used as an explanatory
variable. A similar variable is the
number of uncontested Congressional seats that the incumbent party had in the
previous or current election. State-level studies include variables that
measure the party divisions in the state legislature.
Econometric Studies of the Florida 2000 Presidential Election
After
the Florida 2000 presidential election, statistical estimation of the election
results grew into a cottage industry.[8] Using county level data, various statistical
models have tried to explain either the votes for Bush, Gore, Buchanan, or
Nader. Other studies have focused on the
residual vote. For example, several
papers analyzed irregular votes cast in
Given
the county level data available, these studies have used more specific
socio-economic and demographic data than most of the studies at the national or
state level. Explanatory variables such
as percentage of the county’s population that was white, black, or Hispanic
were included to control for race effects.
Age has been controlled for by including the percentage of the county’s
population over 65 years of age and the percentage of the county’s population
between 18 and 29 year of age. To
control for differences in human capital, the percent of the population with
high school degrees and the percent with college degrees were used as
explanatory variables. The median income
of the county was used as an explanatory variable to control for economic
differences across the counties.
Variation in voting due to sex was captured by including an independent
variable that measured the county’s percent of female population. To explain a given party’s vote, the number
of voters who had previously registered as a member of that party was included
as an explanatory variable. Similar
explanatory variables are used in the empirical analysis that follows.
IV. Data and the Effect of
Voting Technology on Election Outcomes
The
data for this project came entirely from internet sources. County level data on the
As
a first step of analysis, the impact of voting technology on the election
results was examined. For each
Democratic Votesi = β0
+ β1(Registered Democratic Votersi) + β2(PUNCHi)
+ εi (1)
Republican Votesi = β0
+ β1(Registered Republican Votersi) + β2(PUNCHi)
+ εi (2)
Reform Party Votesi =
β0 + β1(Registered Reform Party Votersi)
+ β2(PUNCHi) + εi (3)
Green Party Votesi =
β0 + β1(Registered Green Party Votersi)
+ β2(PUNCHi) + εi (4)
Number of Residual Votesi
= β0 + β1(Number of Voters Who Turned Outi)
+ β2(PUNCHi) + εi (5)
In each of the above specifications,
the first explanatory variable, with a regression coefficient of β1,
is a “scale” variable. Everything else
held constant, an increase in the scale variable should lead to an increases in
the dependent variable, so β1 is expected to be positive.
The
estimation results are reported in Table 3.
Since the Breusch and Pagan (1979) test indicate the presence of
heteroscedasticity in this cross-sectional data set of 67 Florida counties, the
variances of the estimated coefficients were corrected using White’s (1980)
procedure. Notice that the regression
coefficients associated with the “scale” variable are always positive and
highly significant in each of the five regressions. However, β2, the coefficient
associated with PUNCH is only significant in the specification describing the
Green Party vote. This coefficient is
marginally significant at the 10% level, implying Nader got relatively more
votes in counties using the older voting technology. It is also interesting to note that, in spite
of the problems in
Finally,
the residual vote does not appear to be a function of the voting
technology. While β2 in
this specification is positive and approximately equal to 1272, this estimated
coefficient is again not statistically different from zero. This result lends credence to those studies
finding that it was faulty ballot design and instructions, not the voting
technology, that lead to a larger residual vote. Given these initial results that the voting
technology didn’t significantly influence most of the election results, the
next question to consider is the determinants that influence the selection of
voting technology used.
V. The Selection of Voting
Technology: Probit Analysis
Theoretically,
the choice of vote counting technology to use in a given election should be an
endogenous decision. The choice is
affected by the availability and price of each possible counting technology,
the budget of a given government agency, the rate of depreciation and the
vintage of the existing voting machinery used by the county, the tastes of
voters, and the tastes of policy makers.
In a sensitivity analysis, various socio-economic variables were used as
the independent variables in a univariate probit specification. While one must be cautious about data mining,
the goal was to find variables with explanatory power among many possible
independent variables, with theory being inconclusive as to which variables to
include in the model. In general the
specification of the probit model was
PUNCHi = αo
+ α1(selected socio-economic variable) + μi . (6)
The estimation results are reported
in Table 4. The results are not terribly
exciting. The models uniformly lack
explanatory power as evidenced by the low R2. Often the models accurately predicted the
correct choice only 60 to 70 percent of the time. The only socio-economic variable that is
significant at the five percent level or better is counties with relatively
older populations. The estimated slope
coefficient for this variable of 0.77 implies that counties with relatively
older populations are more likely to select the older punch-card voting
technology. This may be indicative of
older citizens’ preference for technology they have used in the past and
possible aversion and mistrust of newer technology. Other results show positive coefficients
associated with population density, the number of registered voters, the number
of registered Democrats, the number of registered Republicans, and the number of
building permits issued that year.
These
results indicate that use of the punch-card machines does not increase with a
relatively larger minority population or a fall in median income. These results
confirm recent findings by Knack and Kropf (2002). However, Knack and Kropf do not examine differences
in ages, and the results in Table 4 indicate that older populations are more
likely to use the punch-type voting machines.
Although
theory is inconclusive as to precisely which variables should be included in a
multivariate specification, the estimation results of one likely specification
are reported in Tables 5 and 6. Table 5
shows that the selection of voting technology was a function of relative age,
the number of local government employees, and the number of nonfarm
establishments in the county. The
positive coefficient associated with a relatively older population is similar
to the result above, and may measure a taste bias towards older
technology. Equally plausible, counties
with older, retired populations may have a smaller tax base, and be less able
to purchase the more expensive voting technology. The results indicate that counties with
larger numbers of local government employees are less likely to choose the
older punch-card voting technology. This
variable may also capture the relative size of the county’s budget. Counties with larger number of employees and
relatively larger budgets may be able to purchase the newer voting technology,
and substitute away from the punch-card technology.
The
economic interpretation behind the number of nonfarm establishments is more
problematic. One plausible
interpretation is that the employees of nonfarm establishments may be
unionized, blue-collar workers - - a traditional Democratic constituent. Did policy makers intentionally select punch-card
machines in this area hoping that Democratic voters would ruin their
ballots? Or, did Democratic decision
makers intentionally choose a technology knowing their core supporters would be
more likely to miscast their votes?
Alas, the interpretation of this result is not easy.
Like
the previous univariate models, the model in Table 5 lacks strong predictive
power. The reported R2 is 17
percent. Table 6 shows that this
multivariate model accurately predicts the counties that adopted punch-card
machines 15 out of 24 times and incorrectly predicts that counties that chose
the older punch card technology would select other technology 9 out the 24
times. Likewise, counties that did not
choose the punch-card technology were predicted correctly 38 out of 43 times,
while these counties were wrongly predicted to choose the punch-card machines 5
out of 43 times. Overall, the model
predicts accurately 70 percent of the time.
The estimation results from this multivariate probit model are used as
the initial starting point - - a “reduced-form” equation - - for the sample
selection models that follow.
VI. Sample
Selection and Estimation of a “Structural –Form” Probit
The
election outcomes in the 2000
The
model separately estimates Democratic votes as a function of registered
Democrats, Republican votes as a function of registered Republican voters, and
residual votes as a function of total voter turnout. The maximum likelihood estimates of the model
are reported in Table 7. Again, for each
equation, the estimates of the “scale” variables are positive and statistically
significant from zero at the five percent level or better. The estimates of rho and sigma are also
reported in Table 7.[13] These estimates are statistically
significant, indicating the presence of sample selection bias, which was
corrected by using the “treatment effects” model.
The
fitted values of the first two models in Table 7 were used to test whether
areas that predominately vote Democratic coincide with counties that use
punch-card voting machines. A
“structural-form” of the probit model was estimated using the predicted values
from the treatment effects models. The
predicted Democratic vote and the predicted Republican vote were obtained. The expected difference in the votes was
formed by subtracting the predicted Republican vote from the predicted
Democratic vote. With PUNCH as the
dependent variable, the expected difference in votes was used as an explanatory
variable in a univariate probit specification, and the results are reported in
Table 8. The negative and statistically
significant slope coefficient implies that a larger probability of a Democratic
majority reduces the likelihood that punch-card voting machines will be
chosen. This finding casts further doubt
on the claim that punch-card machines were intentionally selected for areas
that vote predominately Democratic.
VII. Conclusion
This
paper attempts to apply sample selection, limited dependent variable techniques
to the analysis of the selection of voting machines and the outcome of
elections. Using data from the 67
counties in
The
results from the multivariate probit specification were used as an initial
starting point for a “treatment effects” model that corrects for any sample
selection bias. Results did indicate
that sample selection bias was a problem and, consequently, regressions
explaining the election’s outcome need to control for the choice of voting technology. Finally, estimates from a “structural-form”
probit indicate that differences in expected vote do influence voting machine
choice. For a given county, as the probability
of a Democratic victory increases, the likelihood of choosing punch-card voting
technology decreases. This finding runs
counter to claims that counties with larger democratic
constituencies--minorities, senior citizens, fixed income or low-income
families--saddled their population with “inferior,” older punch-card voting
technology.
These
preliminary results open the door to future work with this data set. The three separate “treatment effects” models
reported in Table 7 beg for a simultaneous equations approach. Additional binary variables can be included
for certain counties to control for differences in ballot design and the
instructions that accompanied those ballots.
Finally, the data set can be used to explain the votes of each county,
and the predictions may be used to forecast who won the election.
References
Alesina, Alberto, John Londregan, and Howard Rosenthal,
“A Model of the Political Economy of the
Alter, Jonathan, “Hey, Relax: We Wuzn’t Robbed,” Newsweek,
Baltimore, David, et al, “Cal Tech – MIT Voting Technology
Project, http://www.vote.caltech.edu .
Barnow, B., G. Cain, and A. Goldberger, “Issues in the
Analysis of Selection Bias,”
Breusch, T. and A. Pagan, “A Simple Test for
Heteroscedasticity and Random Coefficient Variation,” Econometrica,
1979, 47, 1287 – 1294.
Campbell, James, “Forecasting the Presidential Vote in
the States,” American Journal
of Political Science, 1992, 36, 386 – 407.
Fair, Ray, “The Effect of Economic Events on Votes for
President,” Review of Economic and Statistics,
1978, 60, 159 - 173.
Fair, Ray, “The Effect of Economic Events on Votes for
President: 1980 Results,” Review of Economic and Statistics,
1982, 64, 322 - 125.
Fair, Ray, “The Effect of Economic Events on Votes for
President: 1984 Update,” Political Behavior, 1988, 10, 168 – 177.
Fair, Ray, “The Effect of Economic Events on Votes for
President: 1988 Update,”
Fair, Ray, “The Effect of Economic Events on Votes for
President: 1992 Update,” Political Behavior, 1996, 18, 119 - 139.
Fair, Ray, “Econometrics and Presidential Elections” Journal
of Economic Perspectives, 1996, 10, 89 – 102.
Hansen, Bruce, “Who Won
Hansen, Bruce, “A Precinct-Level Demographic Analysis
of Double-Punching in the
Hansen, Bruce, “A Nonparametric Analysis of UnderVotes
in the
Haynes, Stephen and Joe Stone, “Why Did Economic
Models Falsely Predict a Bush Landslide in 1992,” Contemporary Economic
Policy, 1994, 11, 122 – 130.
Kack, Stephen and Martha Kropf, “Who Uses Inferior
Voting Technology?” PSOnline,
September 2002, 541 – 547.
Lewis-Beck, Michael and Tom Rice. Forecasting Elections.
Rosenstone, Steven.
Forecasting Presidential Elections.
Smith, Richard, “A Statistical Assessment of
Buchanan’s Vote in
Tobin, Thomas and Constance Hamburg, “
White, H., “A Heteroscedasticity Consistent Covariance
Matrix Estimator and a Direct Test of Heteroscedasticity,” Econometric,
1980, 48, 817 – 818.
Table 1
Voting Technology Used in the
Type of Technology |
# of Counties |
% of Counties |
% of Population |
Punch Cards Blank paper ballot is inserted into holder labeled with choices and voter indicates choice by poking hole through ballot |
578 |
18 |
32.4 |
Datavote Patented punch-card ballot with choices printed directly on ballot. |
57 |
2 |
4.0 |
Lever Machine Machines that count votes as lever indicating choice is flipped. |
480 |
15 |
18.2 |
Paper Ballots Paper ballots marked by pen and hand counted. |
410 |
13 |
1.4 |
Optical Scan Paper ballot with spaces filled in by voter and read by scanner. |
1,217 |
39 |
27.2 |
Electronic Uses a touch screen similar to ATM machines or handhelds. Votes instantly relayed to and counted by central computer. |
257 |
8 |
8.9 |
Mixed System Counties using two or more of the above technologies |
141 |
4 |
7.9 |
Source:
Table 2
Voting Technology Used in
Type of Technology |
# of Counties |
% of Counties |
Optical Scan |
41 |
61 |
Punch Cards |
24 |
36 |
Lever Machine |
1 |
2 |
Paper Ballots |
1 |
2 |
Percentages
don’t sum to 100 due to rounding.
Source: Division of Elections, Florida Department of State, web page:
http://election.dos.state.fl.us/.
Table 3
The Impact of Using Punch Card Voting Machines on the 2000
|
Dependent Variables |
||||
Independent Variables |
Democratic Votes |
Republican Votes |
Reform Party Votes |
Green Party Votes |
Number of Residual Votes |
Intercept |
-5079.181* (-3.884) |
4051.925* (3.067) |
-3.358 (-0.059) |
202.447* (2.728) |
-973.418** (-2.090) |
Punch Machine Used (1 = Yes, 0 = No) |
2299.006 (0.808) |
-3142.202 (-1.382) |
21.647 (0.440) |
379.669*** (1.863) |
1272.460 (1.428) |
Number of Voters Registered as Democrats |
0.841* (36.226) |
|
|
|
|
Number of Voters Registered as Republications |
|
0.792* (23.358) |
|
|
|
Number of Voters Registered as Reform Party |
|
|
3.678* (3.356) |
|
|
Number of Voters Registered as Green Party |
|
|
|
27.401* (14.439) |
|
Number of Voters Who Turned Out |
|
|
|
|
0.035* (5.190) |
|
|
|
|
|
|
Breusch-Pagan Heteroscedasticity Test |
79.736* |
143.746* |
260.160* |
28.001* |
121.792* |
F Test |
1416.30* |
1203.41* |
40.86* |
234.29* |
62.87* |
R2 |
0.978 |
0.974 |
0.561 |
0.880 |
0.663 |
T-statistics
are in parentheses. Regarding the
asterisks next to the parameter estimates, * indicates the coefficient is
statistically different from 0 at the 1% level, ** indicates the coefficient is
statistically significant at the 5% level, and *** indicates that the
coefficient is statistically different from zero at the 10% level. All of these tests are two-tail tests. The * on the F-test indicates the hypothesis that
all the slope coefficients are equal to zero can be rejected at the 1% level. In every regression, the null hypothesis of
homoscedasticity is rejected at the 1% level.
Standard errors used to form t-statistics were derived using White’s
(1978) consistent estimator.
Table 4
The Determinants of Selecting A Punch-Card Voting Machine: Probit
Estimates
Punchi =
α + βXi + εi
Dependent Variable |
Intercept
(α) |
Slope
Coefficient (β) |
R2 |
Population |
0.313* (4.562) |
2.016E-07 (1.286) |
0.025 |
Population per Square Mile |
0.301* (4.448) |
2.096E-04*** (1.655) |
0.040 |
Number of Registered Voters |
0.288* (4.107) |
5.351E-07*** (1.773) |
0.046 |
Number of Registered Democrats |
0.296* (4.256) |
1.102E-06*** (1.653) |
0.040 |
Number of Registered Republicans |
0.284** (3.965) |
1.456E-06*** (1.784) |
0.047 |
Ratio of Registered Democrats to Registered Republicans |
0.431 (5.542) |
-0.024 (-1.419) |
0.030 |
( % of Population 65 or Older)/(% of Population Between 18 & 65) |
0.111 (0.842) |
0.769** (2.079) |
0.062 |
(% of Population is
Minority)/(% of Population is White) |
0.390 (4.633) |
-0.124 (-0.535) |
0.004 |
(Female Population)/(Male population) |
-0.178 (-0.339) |
0.541 (1.026) |
0.015 |
Median Income |
0.067 (0.195) |
9.381E-06 (0.858) |
0.011 |
% of Population Below Poverty |
0.581* (2.928) |
-0.013 (-1.177) |
0.021 |
% of Population with College Degree |
0.288** (2.095) |
0.889E-02 (0.565) |
0.005 |
% that Own Home |
-0.138 (-0.227) |
6.720E-03 (0.819) |
0.010 |
Number of Local Government Employees |
0.323* (4.751) |
4.340E-07 (1.040) |
0.016 |
|
0.312* (4.473) |
0.367E-08 (1.218) |
0.022 |
Number of Building Permits Issued |
0.288* (4.114) |
2.851E-05*** (1.790) |
0.047 |
Retail Spending Per Capita |
0.177 (1.139) |
2.370E-05 (1.256) |
0.023 |
Number of Employees |
0.314* (4.730) |
5.132E-07 (1.409) |
0.030 |
Number of Nonfarm Establishments |
0.313* (4.709) |
7.158E-06 (1.423) |
0.030 |
T-statistics
are in parenthesis. *, **, and *** indicate the estimated coefficient is
statistically different from zero at the 1%, 5%, and 10% level,
respectively. All tests are two-tail
tests.
Table 5
Determinants of Selecting Punch-Card Voting
Machines: Probit Results
Dependent Variable: Punch ( 1 if Yes, 0
Otherwise)
Independent Variable |
Estimated Coefficient |
Intercept |
-0.927* (-2.262) |
( % of Population 65 or Older)/(% of Population Between 18 & 65) |
0.608*** (1.689) |
Number of Nonfarm Establishments |
9.000E-05* (2.591) |
Number of Local Government Employees |
-6.881E-05* (-2.405) |
|
|
R2 |
0.170 |
T-statistics
are in parenthesis. *, **, and *** indicate the estimated coefficient is
statistically different from zero at the 1%, 5%, and 10% level,
respectively. All tests are two-tail
tests.
Table 6
The Determinants of Selecting Punch-Card Voting Machines: Probit
Results
Frequencies of Actual and Predicted Outcomes
Dependent Variable = Punch ( 1 if Yes, 0 Otherwise)
|
Predicted |
|
|
Actual |
0 |
1 |
Total |
0 |
38 |
5 |
43 |
1 |
15 |
9 |
24 |
Total |
53 |
14 |
67 |
Table 7
Analysis of Probit, Sample Selection, and
Treatment Effects
|
Dependent Variables |
||
|
Democrat Votes |
Republican Votes |
Residual Votes |
Probit Selection Equation |
|
|
|
Intercept |
-0.947** (-2.408) |
-1.892E-02 (-0.080) |
-0.549 (-0.222) |
Number of Local Government Employees |
-2.128E-04** (-2.088) |
-1.654E-04*** (-1.835) |
-7.042E-05 (-0.136) |
|
1.872** (2.054) |
-0.422 (-0.761) |
0.365 (0.071) |
Number of Nonfarm Establishments |
2.764E-04** (2.040) |
2.436E-04** (2.423) |
8.204E-04 (0.117) |
|
|
|
|
Regime Equation Corrected for Treatment |
|
|
|
Intercept |
-419.475 (-0.134) |
-1654.413 (-0.818) |
-1622.858** (-2.105) |
Number of Registered Democrats |
0.868* (44.431) |
|
|
Number of Registered Republicans |
|
0.768* (62.445) |
|
Number of Voters Who Turned Out |
|
|
1.993E-02** (10.034) |
Sigma |
11169.492* (18.207) |
9511.210* (17.656) |
3533.359* (146.642) |
|
-0.625** (-2.220) |
1.000* (477.251) |
1.000* (131.113) |
T-statistics
are in parenthesis. *, **, and *** indicate the estimated coefficient is
statistically different from zero at the 1%, 5%, and 10% level,
respectively. All tests are two-tail
tests.
Table 8
The Impact of Expected Vote Outcome on
Selection of Voting Machines: Probit Results
Dependent Variable: Punch ( 1 if Yes, 0
Otherwise)
Independent Variable |
Estimated Coefficient |
Intercept |
0.408* (6.671) |
Predicted Democrat Votes – Predicted Republican Votes |
-4.257E-05** (-2.299) |
|
|
R2 |
0.075 |
T-statistics
are in parenthesis. *, **, and *** indicate the estimated coefficient is
statistically different from zero at the 1%, 5%, and 10% level,
respectively. All tests are two-tail
tests.
[1] See Knack and Kropf (2002) for a summary and survey of New York Times and Washington Post articles and editorials alleging that voting machines with older technology caused traditional Democratic supporters to miscast their votes. The references of Knack and Kropf (2002) contain a bibliography of the articles.
[2] See http://www.vote.caltech.edu .
[3] Read about the history of voting machines at http://www.infoplease.com/ce6/history/A0851179.html .
[4] See http://www.usatoday.com/news/washdc/2001-02-13-voting.htm .
[5] “Voters Betrayed: No Excuse for Election Foul-Ups,” http://www.miami.com/mld/miamiaherald/news/editorial/4054896.htm.
[6] See “Cal
Tech – MIT Team Finds 35% Improvement in
[7] Examples of these studies include papers by Fair (1978, 1982, 1988, 1990, and 1996), Campbell (1992), Alesina, Londregan, and Rosenthal (1993), Haynes and Stone (1994), Rosenstone (1983), and Lewis-Beck and Rice (1992).
[8] A list of web sites is at http://www.bestbookmarks.com/election/#links.
[9] See Smith (2000) and the papers by Hansen (2000).
[10] See their web site at http://election.dos.state.fl.us/ .
[11] See http://www.census.gov.
[12] See Barnow, Cain, and Goldberger (1981) for an example of a treatment effects model.
[13] The estimate for rho is not a sample correlation coefficient and, for finite samples, the estimate of rho can lie outside [-1,1]. See Greene (1981). When this occurs in LIMDEP, the program uses -1 or 1 in the computations. This is what occurred in the estimation of the results dealing with Republican votes and the residual vote.