One Person No Vote; One Vote; Two Votes: Voting Methods, Ballot Types, and Undervote Frequency in the 2000 Presidential Election*

One Person No Vote; One Vote; Two Votes: Voting Methods, Ballot Types, and Undervote Frequency in the 2000 Presidential Election* Charles S. Bullock, III, University of Georgia M. V. Hood, III, University of Georgia Objectives. Political science long ignored the actual mechanics of voting until the 2000 presidential contest. This research note offers a systematic empirical inquiry into the potential effects of various voting methods and electorate-specific variables on the rate at which citizens register a preference via the act of voting. Methods. Voting methods were analyzed in relation to the rate of undervotes recorded in Georgia s 159 counties during the 2000 general election using a set of multivariate models. Results. Lever machines and fill in the oval optical scan ballots are associated with lower rates of undervoting. Counties with large numbers of new registrants, lower education levels, and a higher proportion of African-American voters were found to have higher error rates. Conclusions. The results of this study provide strong evidence that voting methods and ballot types, as well as electorate-specific characteristics, are key factors in determining the error rate associated with the process of voting at the county level. The 2000 recount in Florida riveted national attention for weeks on problems associated with the casting and counting of votes. The intensive investigation in Florida revealed that failure to register a clear preference by those who intend to cast a ballot may result either from voter confusion or problems with the apparatus used to conduct elections. A third alleged cause of voting problems was racial discrimination as a result of failure to provide assistance to minority voters. Diagnosing the nature of the problem is essential if obstacles to the voting process are to be eliminated. To the extent that voters wishing to register a choice are thwarted because of equipment problems, acquisition of more reliable or more easily operated election systems may remedy the problem. If, however, failure to register a choice stems from voter confusion, the solution may involve voters acquiring greater familiarity with the process. If minority voters are especially likely to confront problems, a more hospitable environment may eliminate racial disparities. *Direct all correspondence to M. V. Hood, III, Department of Political Science, School of Public and International Affairs, 104 Baldwin Hall, University of Georgia, Athens, GA 30602 <th@uga.edu>. The data used in this article are available upon request from the authors. SOCIAL SCIENCE QUARTERLY, Volume 83, Number 4, December 2002 2002 by the Southwestern Social Science Association

982 Social Science Quarterly In this article, we explore the relationship of voting systems and voter characteristics to the incidence of undervoting in Georgia. Georgia is an appropriate setting for this study because its counties used the same four basic types of ballots used in Florida: hand-counted paper ballots, lever voting machines, punch cards, and optical scanners. Moreover, Georgia s Secretary of State Cathy Cox has acknowledged that her state faces the same kinds of problems highlighted in Florida. There, but for the grace of God, go I. In fact, the microscope held up to the antiquated and inaccurate voting systems in Florida would find very similar conditions in nearly every state, including Georgia, Cox warns (2001:56). While Georgia provides a setting similar to Florida, Peach State results have not been affected by court orders or recounts. The disparity between ballots cast and votes tallied is, of course, not due exclusively to faulty election procedures or voter confusion. Some share of the electorate went to the polls with no intention of voting for president; others failed to resolve conflicting feelings about the candidates. The major party choices offered in 2000 may have evoked especially great ambivalence. Throughout the fall, polls reported that the electorate liked Gore s stands on critical issues but preferred Bush on matters of personality and leadership. Many voters who cast a ballot for president remained cross-pressured, as indicated by exit poll results showing that 55 percent of the electorate had reservations about their vote choice. Theory Prior to the 2000 general election, scholarship concerning the effects of voting methods was virtually nonexistent. Subsequently, a team of academics from MIT and Caltech produced an initial report concerning voting equipment and reliability rates. The Caltech/MIT Voting Project analyzed undervotes in presidential elections from 1988 through 2000. Comparing various types of voting equipment employed by counties across the United States, the Caltech/MIT group found that use of punch cards and electronic voting devices was linked to significantly higher undervoting (defined as a vote for more than one candidate, the absence of a vote, or a vote that could not be processed) when compared to paper ballots, optical scanners, or lever machines (Alvarez et al., 2001; Ansolabehere, 2002; see also Posner, 2001). Our study of undervote rates in Georgia extends the research begun in the Caltech/MIT Voting Project in important ways. In addition to believing that voting methods may produce differential rates of undervoting, we test propositions linking the incidence of ballots without a reliable choice to variations in optical scanning equipment. We also include variables to test the possibility that undervoting is attributable to electorate-specific characteristics.

Voting in the 2000 Presidential Election 983 The dominant image from the Florida recount is that of harried election officials squinting at punch cards trying to decipher voter intent. These pictures, the surrounding litigation, and the extended reexamination conducted by the press suggest that counties using punch cards will have higher incidences of undervotes. Problems in registering choices as a result of failure to punch out the chad completely, along with the potential for double voting, contribute to higher rates of unreported votes in counties using this method. These problems led Senator Max Cleland (D-GA) to introduce legislation banning punch-card voting and funds for its replacement. Cleland said of punch-card voting, It s antiquated, flimsy and unreliable (Eversley, 2001:A12). In Georgia, only fully punched ballots were tallied in counties using this method so that undervotes, due to swinging, hanging, or dimpled chads, were maximized. On the other hand, counties using lever machines should have vote totals that come closest to equaling turnout (Alvarez et al., 2001). The lever machines will not permit voters to cast multiple votes in a contest if a voter tries to vote for a second candidate for the same office, the first preference will be undone. Thus the difference between turnout and votes tallied in lever counties indicates the number of voters who did not make a choice and does not include those whose choices went uncounted because of incomplete execution or because of inadvertent double voting. An analysis of 1996 voting found undervoting in heavily African-American precincts to be twice as great when punch cards were used compared with lever machines (Hargrove, 2000). The number of uncounted ballots in counties using optical scanning machines, we anticipate, will be greater than in those using the lever machines but less than where punch cards are used. However, a newspaper-sponsored examination of uncounted ballots in 15 Florida counties concluded that undervoting in counties using optical scanning equipment exceeded that in punch-card counties (Roy and Damron, 2001). Scanners read ballots only when they have been correctly completed. In Georgia, voting on scanner sheets may involve completing an arrow or filling in an oval next to the candidate s name. If the voter places an X or check mark in the oval, circles the oval, or uses a pen or pencil rather than the special marker, the preference will not be recorded. 1 Although some voters in counties using ballots with ovals failed to fill them in correctly, an official in the Secretary of State s office told us that the complete-the-arrow format proved to be more challenging than the other method (Mishou, 2001). Fill-in-the-oval ballots appear familiar to anyone who has taken a multiple-choice test. Connecting the point and butt of an arrow is something that fewer voters have had ex- 1 According to Georgia Secretary of State Cathy Cox (2000), some voters using scantron ballots write in the name of their preference, even though that candidate s name appears on the ballot, and then they place a mark by both the written name and the name printed on the ballot. This results in the ballot not being counted. See also Cooper (2000).

984 Social Science Quarterly perience with and, therefore, we anticipate a higher incidence of undervotes where this approach is used than when voters fill in the oval. Scanners can be programmed to reject ballots when voters mark more than one candidate for an office. The rejected ballot can be presented to the voter, who then has the option of getting a new ballot and voting for only one candidate. The error-rejection function would make a difference only in counties that place a scanner in each precinct since those that do the count centrally after the polls close could not return the ballot to the voter. Most counties with scanners in each precinct did not program the machines to reject double votes because election officials believed that doing so would violate state ballot secrecy protections. However, where double-marked ballots are returned to voters, undervoting should be less frequent. To assess the impact of voting methods on undervoting, other potential causes of failure to register preferences need to be considered. Included among the other possibilities is the prospect that voters may be the responsible party, as opposed to the equipment. Undervotes may result from the failure of individuals to register their preference properly (i.e., an inability or unwillingness to follow instructions). If voters are partly to blame, it should be possible to link certain electorate-specific behavior with the prevalence of undervoting. Those who are more experienced and those who are better educated may have greater success in completing the balloting process. From Florida came assertions that although registration drives signed up thousands of new voters, these participants were especially prone to make errors in the unfamiliar setting of the polling place. To measure the incidence of voters who may be unfamiliar with ballot completion, we calculate the active registrants eligible to participate in the 2000 general election as a percentage of those eligible to vote in the primary election four months earlier. We test the proposition that counties with higher percentages of new voters will have higher rates of undervoting. Education may help voters decipher instructions for completing the ballot so that counties with higher levels of education will have less undervoting (Posner, 2001). To test this hypothesis, we examined two measures of education percentage of the adult population that had completed college and the percentage that had completed high school. In Table 2, college graduate was measured as the percentage of residents in each county who had obtained at least a bachelor s degree. 2 Data for this variable come from the 1990 Census since data for 2000 are not yet available. The Florida experience also gave rise to claims that African Americans encountered discrimination at the polls (but see Ansolabehere, 2002). Some African-American voters in DeKalb County, an Atlanta suburb that for the 2 Substitution of a similar measure for educational attainment the percentage of residents in each county with a high school education did not alter the substantive findings displayed in Models 1 3, Table 2.

Voting in the 2000 Presidential Election 985

986 Social Science Quarterly TABLE 2 Explaining the Undervote in the 2000 Georgia General Election Constant 1.2193*** (0.2498) Voting Method Optical scan 0.1440* (0.0861) Model 1 Model 2 Model 3 1.2193*** (0.2498) 1.2529*** (0.2552) Optical scan error rejection function 0.1570 (0.1770) Optical scan no error rejection function 0.1426 (0.0872) Optical scan connect-the-arrow ballot 0.3755*** (0.1183) Optical scan fill-in-the-oval ballot 0.0315 (0.0887) Punch card 0.3173** (0.1246) Paper 0.2119 (0.2355) Controls % African American registered 0.7038*** (0.2212) % college graduate 4.1251*** (0.7448) % new registrants 1.4786*** (0.5613) 0.3179** (0.1248) 0.2116 (0.2359) 0.7024*** (0.2214) 4.133*** (0.7666) 1.4849*** (0.5655) 0.3042** (0.1231) 0.2105 (0.2233) 0.6401*** (0.2168) 3.9305*** (0.7159) 1.0948** (0.5431) Cragg & Uhler s R 2 0.207 0.207 0.232 N 159 159 159 NOTES: Negative binomial regression coefficients with Huber-White-Sandwich robust standard errors in parentheses; lever machines serve as the comparison category for the models presented. p < 0.10 (one-tailed test), *p < 0.10 (two-tailed test), **p < 0.05 (two-tailed test), ***p < 0.01 (two-tailed test). first time in 2000 was majority African American in registration, claimed that they encountered discrimination when they tried to vote. After the election, seven African Americans filed suit in state court asserting that African Americans faced discrimination in Georgia elections because punchcard machines are disproportionately used in jurisdictions where African Americans are concentrated (Andrews v. Cox, 2001). The complaint in Andrews alleges that the highest rates of undervote occur disproportionately in precincts with high minority populations. An analysis of the 1996 presidential election done by the Scripps Howard News Service found twice the rate of undervoting in heavily minority precincts as nationwide (Hargrove, 2000; see also Gorov, 2000). To assess whether African Americans may have

Voting in the 2000 Presidential Election 987 had more problems recording their preferences, the percent African American among registered voters is included in our models. 3 Data and Methods Data to characterize voting methods in all 159 of Georgia s counties were collected by the authors from the Georgia Secretary of State s Office as well as from election officials in specific counties. A series of dummy variables was created to represent the four types of voting methods utilized during the 2000 general election in Georgia. It is not possible to double vote using a mechanical lever device; thus differences between turnout and preferences in counties using these devices are more likely due to failure to make a selection and not due to voting method. It makes sense, then to use the lever device as the comparison, or excluded, category in the multivariate models presented in Table 2. In addition, the collection of additional information from county election officials made it possible to further separate the optical-scan method by varying attributes. As previously noted, optical scanners can be further categorized according to the type of ballot used and the ability of election officials to program scanners located at the precinct level to reject ballots containing errors. In an effort to draw conclusions about these characteristics and the frequency of undervotes, we created two sets of dummy variables. The first divides counties utilizing optical scanners into two sets, those using a Connect the Arrow ballot and those opting for the Fill in the Oval ballot. A second set of variables divides these same counties according to whether the optical scanners used were programmed to reject erroneous ballots (Error Rejection Function) or not (No Error Rejection Function). The number of undervotes cast in each county served as our dependent measure for the multivariate models presented in Table 2. This variable was calculated by subtracting the votes for all presidential candidates from the total number of votes cast. 4 As observed in Table 1, there is a great deal of 3 Georgia is one of at least five states that maintains registration data by race. 4 Calculated in this manner our measure of undervotes can technically include three different events, two of which are related to voter error. The first event consists of those voters who actually overvoted, or who voted for multiple candidates for the same office (i.e., filling more than one oval on a scantron ballot). A second scenario might involve those voters for whom no preference was registered due to some error on their part (i.e., failing to punch a chad completely through on a punch card). Again, this would result in a situation where the voter s intention was not counted. Finally, some voters might choose not to cast a vote for any of the presidential candidates, but might vote for other down-ticket offices/items. All three of these hypothetical scenarios would result in a vote not being recorded. Unfortunately, data from the Georgia Secretary of State s Office did not allow us to further differentiate among the three events described above, thus preventing separate analysis of undervoting and overvoting such as Posner (2001) did in Florida. Ansolabehere, a collaborator in the Caltech/MIT project, observes, The distinction between undervotes and overvotes may be too fine (2002:62).

988 Social Science Quarterly heterogeneity present when comparing variables of interest at the county level. For example, the number of votes cast varies tremendously among the 159 counties in Georgia. Taliaferro County recorded only 881 votes compared with 280,975 votes cast in Fulton County. Other variables of interest, such as the number of undervotes or the percentage of African Americans registered to vote, also vary greatly both within, and across, counties. Such disparities can lead to problems associated with unobserved heteroskedasticty produced by a heterogeneous clustering of the population at some subcounty level (i.e., voting precincts). A second problem that can affect analyses at the county level is that of aggregation bias. Given that counties are fairly large geographic units, many substantive variables of interest may actually be proxies for one another. For example, the percentage of African Americans registered to vote at the county level may also be highly correlated with other demographic variables, such as urban/rural distinctions. If more African Americans are registered to vote in urban counties than in rural counties, then one may falsely substitute the observed correlation between African-American registrants and the undervote rate for the relationship between urbanization and undervotes. If these same factors are also associated with certain types of voting equipment (i.e., urban counties and the deployment of punch-card devices), it is easy to see the added complexity involved in attempting to draw valid causal inferences. Although we readily acknowledge the potential for this problem in this research note, we have little alternative but to conduct our analysis at the county level as data on undervotes in Georgia is not currently available at the precinct level. 5 Using the number of undervotes as our dependent variable necessitates the use of an estimation technique designed specifically to deal with countylevel data. The most commonly used approach is to estimate a model using Poisson regression. Tests on our data reveal the presence of overdispersion, or a situation where the conditional variance exceeds the conditional mean (Cameron and Trivedi, 1998:77). In cases where overdispersion is present, a variant of Poisson known as negative binomial regression is utilized to correct for the potentially biasing effect produced by unobserved heterogeneity (see McCullagh and Nelder, 1992 or Cameron and Trivedi, 1998 for a more detailed discussion of these techniques). 6 5 In an effort to ensure that our models were properly specified, we included a number of other controls. Variables denoting level of urbanization at the county level and the number of voting precincts within a county were utilized in an effort to control for other potentially relevant factors (i.e., the relative size of the voting district as denoted by the number of precincts present). These controls never attained statistical significance and did not alter the other substantive results presented and were, consequently, removed from the models. 6 Models presented in Table 2 were calculated using the nbreg procedure in Stata 7.0. The total number of votes cast for each county was used as an offset or exposure variable for the models presented in Table 2. For purposes of comparison, the models presented in Table 2 are reproduced in the Appendix using OLS regression. The dependent variable for these

Voting in the 2000 Presidential Election 989 Findings In the 2000 election, Georgia counties used four methods of voting. As Table 1 reports, lever machines developed about a century ago and not manufactured in more than a generation are used in 73 counties and tallied just over a 10th of the ballots. Optical scanning, the newest approach available in the state, was found in 67 counties, which counties contained a majority of the state s voters. Although only 17 counties voted with punch cards, this method was used in several of Georgia s most populous counties and accounted for 30 percent of the ballots in the 2000 presidential election, compared with one-third of the nation s precincts that reported using this approach in 1998 (Eversley, 2001). Finally, two rural counties still used hand-counted paper ballots. The incidence of undervoting in the presidential election ranged from zero in two counties that used lever machines to a high of almost 19 percent. As reported in Table 1, the statewide figure is about 3.5 percent, which is almost twice the 2000 national average (Rankin, 2001) and the 1988 2000 mean (Alvarez et al., 2001). As anticipated, undervotes were most frequent in counties using punch cards, where more than 4.5 percent of the ballots did not contain a valid preference for president. Surprisingly, the fewest undervotes occurred not on lever machines but when opticalscanning equipment was used, even though the connect-the-arrow ballot proved as much of an obstacle as the punch card. Optical scanners using the fill-in-the-oval ballot had the lowest undervote rate among all the methods analyzed, at 2.29 percent. Even this method, however, had a higher incidence of undervotes than the national average. Table 1 shows essentially no difference in undervote rates when counties that rejected double votes are compared with counties using scanners that did not return double-marked ballots to voters. Model 1 in Table 2 examines the undervote count comparing the four methods of voting utilized in Georgia. The multivariate model results produce a slightly different picture when compared to the descriptive statistics presented in Table 1. As hypothesized, in comparison to the mechanicallever method, both punch cards and optical-scanning equipment were significantly more prone to undervoting. While coefficients in count models are not as directly interpretable as OLS regression coefficients, they can be converted to a form amenable to comparison. For example, in comparison to counties using lever machines, those relying on optical scanners can expect to see about a 15.5 percent increase in the number of undervotes. Likewise, use of punch cards is estimated to cause a 37 percent increase in the number of undervotes observed. models is the percentage of undervotes cast in each county (Total Undervotes/Total Vote Count).

990 Social Science Quarterly Model 1 also demonstrates that all three electorate-specific variables were significant determinants of the number of undervotes. Counties in which African Americans composed higher percentages of the electorate or that had larger numbers of new voters had higher undervote counts. In contrast, counties with a more educated electorate, defined as higher percentages of citizens with a college education, had lower numbers of undervotes. The relative size of these electorate-specific effects is quite substantial when compared to the impact of voting methods. For example, a one standard deviation increase in the proportion of county residents with a college degree would decrease the undervote count in a given county by an estimated 20.9 percent. Electorate-specific characteristics can have a profound effect on the rate of undervoting, regardless of the voting method employed. Model 2 differentiates optical-scanning equipment by identifying those configured to reject, or kick out, ballots containing errors. The second category contains all other scanning configurations, including those tallied at a central location and those precinct-level scanners that do not reject erroneous ballots. Model 2 has variables indicating the presence/absence of a kickout function along with indicators for use of paper or punch-cards methods. The results of Model 2 indicate that there is some evidence to support the contention that optical-scan counties that did not screen for errors at the time a vote was cast did have more undervotes compared to the comparison category. Counties using optical scanners programmed for error rejection, in contrast, are not significantly different in statistical terms from counties using lever machines. As in Model 1, the punch-card method continues to display a higher occurrence of undervoting, while electorate-specific characteristics persist as significant determinants of undervoting. Model 3 distinguishes between the types of optical-scan ballots, with counties divided into those that used Connect the Arrow and those with Fill in the Oval. Counties in which voters had to demonstrate their preferences by connecting an arrow had higher rates of undervotes. Voters whose county required them to darken in an oval on the ballot in order to register a preference were no more likely than voters utilizing lever machines to fail to register a valid choice. All three of the electorate-specific variables continue to exhibit significant and expected results. Finally, it should be noted that counties using punch cards, ceteris paribus, actually had lower rates of undervoting than counties using optical scanners with the connectthe-arrow ballot (a 45.6 percent increase vs. a 35.6 percent increase, respectively). Conclusion This analysis of Georgia s 2000 election examines multiple explanations for undervoting. The equipment in use plays a role, but even with the most user-friendly approach available, tens of thousands of ballots made no

Voting in the 2000 Presidential Election 991 choice for president. This suggests that even upgraded electoral systems will continue to have a substantial undervote. Of course, some undervotes result from voters who find none of the choices attractive. Ralph Nader s absence from Georgia s ballot may account for some of the disparity between turnout and votes for president. The analysis also suggests that electoral experience may be a factor. Regardless of voting method, undervotes were more common where recent expansion of the electorate had been greatest. In addition, more undervotes occurred in counties where the electorate was less educated. If first-time voters are more prone to fail to register preferences, they will become increasingly likely to complete the process as they gain experience. The correlation between percent African American and undervoting may be the product of race-related problems, although more evidence is needed before one can conclude that discrimination exists. Perhaps uncertain African-American voters were reluctant to seek assistance from white poll workers. The record level of African-American turnout may have overtaxed facilities in heavily African-American precincts and reduced the availability of assistance. The county-level results coincide with charges in Andrews that undervotes were more prevalent in heavily minority precincts. The third model in Table 2 provides insights for election officials. Although nothing here sheds light on the merits of an ATM-style system, 7 it does indicate the relative advantages of alternative optical-scan systems. Undervoting is reduced when fill-in-the-oval rather than complete-the-arrow ballots are used. Precinct scanning with an overvote-rejection function enabled also results in fewer ballots lacking a clear preference, but is less a factor than the way in which the optical-scan ballot is marked (i.e., ovals vs. arrows). Surprisingly, however, nothing in our analysis shows that undervotes are reduced by technological advances, such as optical scanning. This format never has fewer undervotes than do the lever machines that have been out of production for decades. REFERENCES Alvarez, R. Michael, Stephen Ansolabehere, Erik Antonsson, Jehoshua Bruck, Stephen Graves, Nicholas Negroponte, Thomas Palfrey, Ron Rivest, and Charles Stewart. 2001. A Preliminary Assessment of the Reliability of Existing Voting Equipment. Available at <http://www.vote.caltech.edu/reports/report1.pdf>. Andrews v. Cox. 2001. Civil Action File No. 2001CV32490, Superior Court of Fulton County. Ansolabehere, Stephen. 2002. Voting Machines, Race and Equal Protection. Election Law Journal 1:61 70. Cameron, A. Colin, and Pravin K. Trivedi. 1998. Regression Analysis of Count Data. Cambridge: Cambridge University Press. 7 Alvarez et al. (2001) report that ATM-type electronic machines perform as badly as the punch cards.

992 Social Science Quarterly Cooper, Richard T. 2000. A Different Florida Vote In Hindsight. Los Angeles Times December 24:A1. Cox, Cathy. 2000. Talk to political science class at University of Georgia, November 30. Athens, GA.. 2001. Cox Urges Pilot Testing of State-of-the-Art System. Georgia Trend 16:56 57. Eversley, Melanie. 2001. Cleland Plans End to Punch-Card Votes. Atlanta Journal January 26:A12. Gorov, Lynda. 2000. Black Areas Had the Most Ballot Problems. Atlanta Journal- Constitution December 2:A15. Hargrove, Thomas. 2000. Minority Votes Often Miscounted. Atlanta Journal December 28:A6. McCullagh, Peter, and John A. Nelder. 1992. Generalized Linear Models. New York: Chapman Hall. Mishou, Tom. 2001. Telephone interview. Posner, Richard A. 2001. Breaking the Deadlock. Princeton, N.J.: Princeton University Press. Rankin, Bill. 2001. Uniform Voting System May Meet Opposition. Atlanta Journal January 3:B6. Roy, Roger, and David Damron. 2001. Small Counties Wasted More than 1,700 Votes. Orlando Sentinel January 28:electronic edition.

Voting in the 2000 Presidential Election 993 APPENDIX Explaining the Undervote in the 2000 Georgia General Election Model 1 Model 2 Model 3 Constant 0.0295 0.0293 0.0104 (0.0305) (0.0305) (0.0270) Voting Method Optical scan 0.0107* (0.0049) Optical scan error rejection function 0.0097 (0.0077) Optical scan no error rejection function 0.0108* (0.0050) Optical scan connect-the-arrow ballot 0.0238** (0.0058) Optical scan fill-in-the-oval ballot 0.0046 (0.0044) Punch card 0.0135** 0.0135** 0.0125* (0.0051) Paper 0.0069 (0.0092) (0.0051) 0.0069 (0.0092) (0.0061) 0.0068 (0.0157) Controls % African American registered 0.0342** (0.0121) 0.0342** (0.0121) 0.0310** (0.0119) % college graduate 0.1569** (0.0289) 0.1563** (0.0288) 0.1470** (0.0315) % new registrants 0.0670* (0.0278) 0.0697* (0.0277) 0.0525* (0.0250) R 2 0.234 0.234 0.281 N 159 159 159 NOTES: OLS coefficients with Huber-White-Sandwich robust standard errors in parentheses; lever machines serve as the comparison category for the models presented. *p < 0.05 (two-tailed test), **p < 0.01 (two-tailed test).