Man vs. Voting Machine: The 2000 Florida Presidential Election

 

 

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

Arkansas State University

 

 

June 2003

 

 


Man vs. Voting Machine: The 2000 Florida Presidential Election

 

 

I.          Introduction

            After the 2000 presidential election in Florida, the word “chad” - - hanging, dimpled or pregnant - - was introduced to the American political lexicon.  With the close election between George W. Bush and Al Gore, the accuracy of the voting machines used in Florida was questioned.  The large number of ballots that the voting machines rejected and, consequently, were not included in the final tally was also a concern. In the aftermath of the election, some argued that the punch-card voting machines, which embodied older technology, were intentionally selected with the hope that traditional Democratic constituents would make mistakes during voting and ruin their ballots.  It was alleged that the punch-card voting machines would confuse voters, leading to either no votes being cast, votes being cast for more than one candidate, votes being cast for the wrong candidate, or improper use of the machine leading to inability to count a cast vote.  Proponents of this argument contend that these machines were selected to increase the number of spoiled ballots among Democratic voters, causing these votes not to be included in the final vote count, and increasing the likelihood of a Republican victory.

            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 Florida was the climax of “a decade of Democrats around the county slitting their own throats by doing nothing to discard the punch-card election system . . . that consistently disenfranchises their most loyal supporters (Alter, 2000).”

            This paper attempts to quantify the socio-economic factors that affected the selection of the voting machines used in each of Florida’s counties during the 2000 election.  Univariate probit specifications generate mixed results.  One of the strongest statistical results is that counties with older populations have been more likely to select punch-card technology.  One multivariate probit specification suggests that counties with smaller government budgets populated by relatively older populations and more nonfarm business establishments are more likely to select punch-card voting machines.

            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 America, there were between 4 and 6 million votes lost in the 2000 presidential election.[2]  The residual vote is a proxy for the no vote and the number of spoiled ballots.  This paper shows no statistically significant link between the use of punch-card voting machines and the size of the residual vote.  This finding confirms other conclusions that it was not the voting technology that lead to a higher residual vote but the poor design of ballots and flawed sets of instructions that accompanied them (Tobin and Hamburg, 2001).

            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 United States, in general, and used in Florida during the 2000 presidential election, in particular.  Next, given the attempt to econometrically analyze the selection of the machinery and the outcome of the election, the third section of the paper offers a brief review of the relevant literature in economics and political science.  The fourth section of the paper discusses the data and its sources and also contains a simple ordinary least squares analysis of the impact of voting technology on the election outcome.  The fifth section of the paper discusses the selection of the voting technology and the use of limited dependent variable econometric techniques.  The results of the sample selection estimation and the estimation of a “structural” probit equation explaining the selection of voting technology is in the sixth section of the paper.  The final section of the paper offers a critique of the results and thoughts on future work.

 

II.        Voting Machines in the U.S. and in Florida

            Since their inception in the state of New York in 1892, voting machines have commonly been used throughout the United States.  This use of machines is a uniquely American practice, as they are rarely used in other countries.  The costs of the technology, infrequent elections, and simpler ballots diminish the practicality of using voting machines in other countries.[3]  The use of voting machines in the U.S. grew for several reasons.  It led to faster tabulation of the votes, it minimized human error, and perhaps most importantly, it reduced the opportunities for voting fraud.  However, there are complaints that some would-be voters find the machines intimidating.  The recent troubles during the 2002 primary in Florida show that even new technology comes with a start-up cost.  Break down is frequent and delays are possible.  Finally, the chance for fraud still exists.

            Table 1 lists the various type of voting technology used in the United States.  These technologies include the traditional paper ballot, the mechanical machines that entail flipping a lever, punch-card machines, ballots that are read by a scanner, and the newer electronic technology involving computers.  Punch-card technology is used by approximately 36 percent of all Americans, while 27 percent of the population has access to the optical-scan technology.  While the new electronic voting techniques are used by nearly 9 percent of the country’s population in 8 percent of the nation’s counties, the use of the optical-scan technology has experienced the most rapid growth.

            As shown in Table 2, during the 2000 presidential election there were no electronic voting machines in Florida.  Of Florida’s 67 counties, 61 percent selected the optical scan voting technology, and 36 percent selected the punch-card type technology.  The remaining two counties used either paper ballots or mechanical machines. 

            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 Florida, the conversion to newer voting technology brings the potential for increased frustration.  In an editorial saying that voters were betrayed, the Miami Herald wrote of poll workers who were unfamiliar with the new touch-screen technology and misplaced computer-voting cartridges.[5]  On the other hand, officials at the Cal Tech – MIT Voting Technology Project report that the new touch-screen technology used recently in Florida resulted in a decrease in the residual vote.  They found that the residual vote among Democratic voters fell from an average of 3.1 percent of Democratic votes to 2 percent - - a 35 percent improvement in registering votes cast.[6]  Since one of the paper’s goals is to determine the impact of a given voting technology on the outcome of the election, the next section reviews econometric studies of elections.

 

III.       Literature Review: Econometric Studies of Elections

            The econometric analysis of U.S. presidential elections takes one of two forms.  First, empirical studies analyze presidential elections at the macro level, explaining the determinants of winning the national election.  After the Florida debacle in the 2000 presidential election, analysts turned to the micro level, attempting to explain the determinants of voting at the county level.  Each of these branches in the literature will be discussed in turn.

 

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 Palm Beach County.[9]

            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 Florida 200 election results and the voting technology used in each county at that time came from Florida’s Secretary of State’s Division of Elections.[10]   All the various socio-economic and demographic measures of the Florida counties come from the state and county “Quick Facts” data online with U.S. Bureau of Census.[11]

            As a first step of analysis, the impact of voting technology on the election results was examined.  For each Florida county, a variable named PUNCH was defined.  PUNCH was equal to one if the county used the punch-card type voting machines; otherwise PUNCH was set to zero.  The five specifications below were estimated using ordinary least squares.

 

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 Palm Beach county where some claim faulty ballot design caused voters to miscast their ballots for Buchanan and the Reform Party, β2 is positive, but statistically insignificant.

            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 Florida presidential election were subject to a “treatment” - - the choice of voting technology.  A treatment effects model is used to determine whether there is any sample selection bias in the estimates.[12]  An example of a treatment effects model is a study of the annual income of workers when a subset has received the “treatment” of a college degree.  The econometric procedure considers both the choice of getting a college degree and how it impacts earnings.  Likewise, in the following model, election outcomes are explained in light of the voting technology used.

            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 Florida from the 2000 presidential election, regressions corrected for heteroscedasticity indicate that the choice of voting machine did not affect the number of Democratic votes, Republican votes, Reform Party votes, or the number of residual votes.  Using a probit specification, it was found that counties with relatively older populations were more likely to use punch-card voting machines.  However, other socio-economic variables - - race, gender, and income - - lacked explanatory power in describing the choice of election machinery.  Using a multivariate probit specification, it was found that punch-card voting machines were more likely to be used in counties with older populations, smaller local government budgets, and larger numbers of nonfarm establishments.

            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 United States,” The American Political Science Review, 1993, 87, 12 -233.

 

Alter, Jonathan, “Hey, Relax: We Wuzn’t Robbed,” Newsweek, November 27, 2000, p. 47.

 

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,” University of Wisconsin, Madison, WI, 1981.  Mimeographed.

 

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,” Yale University, New Haven, CT, 1990.  Mimeographed.

 

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 Florida?  Are the Palm Beach Votes Irregular?” University of Wisconsin, Madison, WI, 2000.  Mimeographed.

 

Hansen, Bruce, “A Precinct-Level Demographic Analysis of Double-Punching in the Palm Beach Presidential Vote,” University of Wisconsin, Madison, WI, 2000.  Mimeographed.

 

Hansen, Bruce, “A Nonparametric Analysis of UnderVotes in the Palm Beach Presidential Vote: Implications of a Recount,” University of Wisconsin, Madison, WI, 2000.  Mimeographed.

 

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.  Washington, D.C.: Congressional Quarterly Press, 1992.

 

Rosenstone, Steven.  Forecasting Presidential Elections.  New Haven: Yale University Press, 1983.

 

Smith, Richard, “A Statistical Assessment of Buchanan’s Vote in Palm Beach County,”  University of North Carolina, Chapel Hill, NC, 2000. Mimeographed.

 

Tobin, Thomas and Constance Hamburg, “Florida’s Confusing Ballots,” St. Petersburg Times, November 11, 2001.

 

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 United States

 

 

 

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: U.S. Today, http://www.usatoday.com/news/politics/votingindex.htm, 9/14/02.


Table 2

Voting Technology Used in Florida During 2000 Presidential Election

 

 

 

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 Florida Presidential Election: OLS Results

 

 

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

Funds County Receives from Federal Government

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)

Rho

-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 Florida’s Voting Technology,” http://pr.caltech.edu/media/Press_Releases/PR12284.html .

 

[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.