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New Voting Systems for NY —Long Lines and High Cost

by William A. Edelstein, Ph.D.
Member, Board of Directors
New Yorkers for Verified Voting
November 14, 2006


As New York decides on new voting systems, one key question is this — how many voters can be served by each voting machine? This number is critical in order to estimate costs as well as to avoid long lines for voters. The New York City Board of Elections recently released a report saying that New York should replace each lever machine by 1 full-face-ballot computer DRE voting machine with voter verified paper trail. Assuming that each voter will take 3.25 minutes to vote, they calculate that 277 voters can vote on each DRE in a 15-hour election Day. However, the report neglects the effect of non-uniform voter arrivals, DRE outages and extra time needed by voters using special accessibility aids on DREs. We have applied queuing theory, the mathematical study of waiting lines, to carry out computer simulations of realistic elections. We use a scenario with more voters arriving at peak times—early morning, lunch and early evening hours—as is typical during elections. According to our calculations, a ratio of 277 voters per DRE would cause unacceptable wait times of 1-hour or longer. Recent elections with DREs have produced extremely long lines in many places around the country, causing would-be voters to leave, thereby disenfranchising them. In order to guarantee reasonably short wait times—even without taking into account DRE outages and the use of DRE special voting aids—our results indicate that each DRE in New York should be allocated to no more than 150 voters, which means replacing each lever machine by 3 DREs. But the acquisition and maintenance cost of this many electronic voting machines would be excessive. In contrast, precinct based, paper ballot optical scan systems use simple, inexpensive marking booths that are the equivalent choke points to DREs. These paper ballot scan systems can be easily and economically configured to eliminate lines.

Voting system choice: timing is everything

Early in 2007, New York counties will choose either direct recording electronic voting machines (DREs) or paper ballot-scanner systems (PBOS) to replace lever voting machines. How many new voting machines will be needed? The answer to this question is critical for ensuring that each county's voting will go smoothly and that costs will be within reason.

Long lines have occurred during elections with DRE use in California, Florida, Maryland, Mississippi, Ohio, Pennsylvania, Tennessee, Utah and other states1-9 and have caused some voters to give up and go home, effectively disenfranchising them. It is prohibitive to buy a large number of DREs because of their cost, which makes it likely that a substantial number of voters using DREs will end up in long lines. In contrast, PBOS uses inexpensive marking booths whose numbers can be increased to eliminate lines and long waits.

Long voter waits—and consequent disenfranchisement of those who cannot wait—may prove to be a fundamental and disqualifying problem for DREs.

The New York City Board of Elections recently published a report entitled "An Analysis of the Number of Voters per Voting Machine"10 which omits several important considerations and contains a number of doubtful assumptions. The result is a serious underestimate of the number of DREs that would be needed to serve the voters of New York City as well as a misunderstanding of relevant aspects of paper ballot-scanner systems.

The New York City Board of Elections report:

  • Incorrectly assumes that a maximum of 50% of voters will appear at any election;
  • Does not take into account the extra time needed to vote on DREs by persons with disabilities;
  • Does not take into consideration the uneven arrival of voters, particularly during peak voting hours, and potential voter traffic jams;
  • Does not include the effects of machine and procedural breakdowns.

Properly taking these factors into account substantially decreases the number of voters that could use a voting machine in a day and considerably increases the number of DREs that would have to be purchased and maintained.

In their examination of the use of DREs in the recent Cuyahoga, Ohio primary, the Election Science Institute carried out a queuing theory analysis of the potential for long lines.11 Following their approach, we have done our own queuing theory simulation of voting statistics. If we accept the New York City Board of Election report’s figure of 3.25 minutes to vote on a DRE with voter verifiable paper trail—which the report claims will allow 277 voters to use a single machine in a 15 hour voting day—then our study shows that a significant fraction of such elections will have maximum voter waits of over an hour to cast their ballot. This will happen even without the all too common experience of DRE breakdown; it also will occur even if we do not factor in extra time for voters with disabilities. Details of our calculations are given in the full report.

The only way to guarantee short lines is to have a large overcapacity, i.e., to have many more voting systems than would be needed for the average voter flow. This is not practical with DREs because of their high cost. However, New York counties could avoid long lines and save money by choosing paper ballot scanner systems. In the 2004 general election, Lee, Massachusetts accommodated 3200 voters on a single paper ballot scanner12 and Londonderry, New Hampshire13 processed more than 12,000 voters on two scanners in a 13 hour Election Day. Voters mark their ballots in inexpensive marking booths, and there were no lines waiting to mark ballots or to use the scanners in these towns. The number of marking booths can be increased at low cost to avoid any problems of voter traffic congestion and long lines.

Factors not fully considered by the New York City report

Voter turnout will be significantly higher than 50% at some pollsites

The New York City report10 assumes that a maximum of 50% of registered voters will appear in any election and calculates the number of machines they will order based on this assumption. While the average turnout for New York’s 5 counties (New York, Bronx, Kings, Queens and Richmond) was indeed 50% in the 2004 general election, many areas had higher figures.14,15 So to guarantee efficient access to the polls, it is necessary to consider the peak vote, which could occur in any election precinct.

Figure 1. Number of New York City Assembly Districts vs. % turnout in the 2004 general election. Each bar represents how many Assembly Districts had turnout in the range covered by the bar. There were 6 districts that had turnout between 40%-42%, 5 districts had turnout between 42%-44%, 1 district between 44%-46%, etc.

Figure 1 shows the number of Assembly Districts in New York City Counties vs. their votes for President in the 2004 election.14,15 There are many Assembly Districts where the turnout was well above 50%, indeed approaching 60%. Since these are averages over Assembly Districts, it is apparent that some election precincts within these Districts must have had higher turnouts than 60%. Statewide, over 60% of voters showed up. (The Lee, MA and Londonderry, NH examples cited above had over 80% turnout in 2004.)

The 2004 NY data suggests that an estimate of 75% as an upper bound for voter turnout would be appropriate. This is the same percentage that has been used by New York City to determine how many lever voting machines should be deployed. An underestimate of the number of machines could lead, at least, to serious voter traffic flow problems, long waits and extended Election Days. At worst, it can lead to voter disenfranchisement.

This occurred in the 2004 general election in Florida and Mississippi.1,2 In Ohio long lines caused voters to give up and leave without voting.4 There were more long lines in the recent 2006 primary in Cuyahoga County, Ohio.11 There were long lines—along with other DRE issues—in the September 2006 problematic primary in Maryland.3 Insufficient DREs and DRE malfunctions caused more long lines and voter frustration in a number of places in this year’s general election on November 7 (e.g. refs. 5-9).

People with special needs will take much longer than 3.25 minutes to vote on DREs

The New York State Board of Elections studied the time needed for persons with special needs to vote with ballot marking devices.16 This varied from 18 to 45 minutes among the several systems and types of accessibility aids considered. Voting on DREs using accessibility aids would be similar.

The New York State Board of Elections (NYBOE) has hired the American Institutes for Research (AIR)17 to test voting machines and answers are supposed to be coming in the next few months. Part of their charge is to estimate how many voters would use accessibility aids. This would include, for example, voters with visual, dexterity, or mobility impairments who would use the audio interface or sip and puff controls. It might also include voters who are not comfortable with computers, touchscreens, or the use of English.

A small number of voters with special needs, each taking 30 minutes to vote, would have a profound effect on numbers of voters able to use a DRE on Election Day.

Voters do not arrive at exact intervals

The New York City report allots an average of 3.25 minutes for each voter to use a DRE with voter verifiable paper record. 900 minutes (a 15 hour Election Day) divided by 3.25 is 277. They then assert that a single DRE can accommodate 277 voters, and propose to buy one DRE for each 554 registered voters on the basis of a 50% turnout. However, the New York City report does not properly take into account the effect of fluctuations of voter arrival. It says:

On Election Day, there are "peaks and valleys" of usage by voters depending upon the time of day, the weather, traffic and other variables outside of the control of election staff. Thus there will always be times when voters are waiting, but on the whole, there should be some insurance that waits will not be over long durations throughout the day and that on the whole, voting can be accomplished expeditiously. If we make the assumption that on the whole elections are conducted expeditiously by the survey jurisdictions, than [sic] a maximum that is at, or somewhat higher than, the average by type of technology should be a reasonable maximum for New York.10

These unsupported assumptions are contradicted by DRE delays around the country1-9 and the mathematics of queuing theory that governs the voting process.

We begin our election simulation by assuming 277 voters per DRE estimated by the New York City report. We take a scenario with heavy voter arrivals from 6am to 8am, 12pm to 1pm and 5pm to 7pm, where voters arrive at double the rate of the rest of the day, and no DREs break down. If the whole-day average is 18.5 arrivals per hour, then the slow periods will have 14 per hour and the fast periods 28 per hour.

There will be many voting locations where only a small number of DREs will be needed,10 so we have focused—as examples—on pollsites with 1, 2 or 4 DREs. Sites with more DREs will behave proportionally.

With these conditions, over 80% of precincts with 1, 2 or 4 DREs will have voters waiting for more than an hour. Voters will have a maximum wait of more than 1-1/2 hours in 38%, 17% and 3% of precincts where there are 1, 2 or 4 DREs, respectively.

If we have 150 voters per DRE—approximately the ratio of privacy booths to voters specified by statute in NH, scaled by the different Election Day lengths in NH (13 hours) and NY (15 hours)—then there will be few voters waiting more than thirty minutes.

DREs and printers will break, need rebooting, or otherwise cause delays

DRE outages will cause further delays. The present reliability guidelines allow over 9% of voting machines to fail in a 15-hour day,18 and ESI uses a one-hour average repair/replacement time in some of their calculations.11

The bottom line is that even with many more DREs than recommended by the New York City report,10 queuing statistics guarantee that a substantial number of voting precincts will have voters with very long waits. In order to avoid long lines at DREs for all precincts, it is necessary to have a large excess capacity of voting machines. With DREs, this is not realistic because of their high acquisition and operating costs.

Paper Ballot/Optical Scan: Londonderry, New Hampshire and Lee, Massachusetts

The following examples of voting by paper ballots and ballot scanners show how PBOS systems can eliminate long voter queues at a minimal cost.

Lee, Massachusetts uses PBOS. They had 4,000 registered voters and 3,200 (80%) used 35 privacy booths and one scanner in the 2004 election. The Lee town clerk says that they had no lines at the privacy booths in the 2004 election, whereas they had "long, long lines" when they had previously used 8 lever machines.12

Londonderry, New Hampshire has 15,029 registered voters and 12,229 (81%) of them voted in the 2004 election.13 They use PBOS and have two scanners. Each scanner therefore processed about 6114 ballots which is equivalent to 7055 ballots in a 15-hour day. (Note--even if we changed this by a factor of two to accommodate undervote notification in NY, each scanner could still handle 3527 ballots in a day.)

Londonderry has 100 privacy booths, each of which served an average of 122 people in their 13 hour Election Day in 2004, equivalent to 141 voters per NY’s 15 hour Election Day. The town clerk said that there were no lines at the privacy booths. New Hampshire requires a privacy booth for every 125 voters. Just in case more voters show up, she has extra cardboard privacy screens that can be placed on tables.

During a heavy election, the Londonderry town clerk estimates that only 10% of booths will be filled much of the day but 90% are occupied during peak times.

Since the scanners only count ballots but do not record the votes, a stopped scanner does not halt the election, unlike DRE failures. If the scanner is down, the ballots are placed in a special compartment in the ballot bin and scanned later. The Londonderry town clerk has supervised 25-50 elections over the last 7 years and has experienced only one scanner breakdown. A replacement scanner was brought over and put into service in less than an hour.

These examples show the kind of overcapacity that works. It is easy to achieve with PBOS since the privacy booths cost about $150 each. In reality, it would take more than 100 DREs in Londonderry, New Hampshire or 35 DREs in Lee, Massachusetts to achieve the same ease of use since 1) DREs have a much greater breakdown rate than scanners and 2) voters with disabilities would take up a lot of DRE capacity. In contrast, ballot marking machines that go with PBOS are separate devices that do not affect flow of voters in other privacy booths or the operation of the scanners.

How many voting machines do we need?

Direct Recording Electronic Voting Machines (DREs)

The New York City report suggests that each DRE could serve 277 voters on Election Day. Assuming a 50% turnout, they conclude that one DRE should be purchased for each 554 voters, which is not too different from what the report says is an average of 1 lever machine for 600 voters. In other words, they recommend replacing each lever machine by a single DRE.10

Our study shows that 277 voters per machine is unrealistic (given the New York City voting time figure of 3.25 minutes) and will lead to very long waiting times in some election districts. We believe a realistic ratio that keeps lines down everywhere would be more like 150 voters per DRE. Trying to serve even this number of voters with one DRE may prove problematic because of DRE outages and long voting times for persons with special needs. Taking 150 voters per DRE and a possible 75% turnout implies a DRE for each 200 registered voters. The replacement ratio then becomes 3 DREs for each lever machine.

The time for each person to vote (3.25 minutes) in our calculation was taken from the New York City report and could change when the "usability study" is completed by AIR. Any figures then obtained can—and should—be used for a queuing analysis similar to what we have done here.

Paper Ballot, Ballot Marker, Optical Scan Systems (PBOS)

The examples above from Londonderry, New Hampshire and Lee, Massachusetts demonstrate that a large overcapacity, i.e. one privacy booth for 125 voters (Londonderry, New Hampshire ) or per 90 voters (Lee, Massachusetts) essentially eliminated the experience of voting bottlenecks. This is a simple and inexpensive solution which would improve the voting experience in New York, as it did when Lee, MA went from 8 lever machines for 3200 people to 35 privacy booths.

If we scale the New Hampshire number from a 13 hour day to a 15 hour day, then one needs approximately one privacy booth for each 150 voters who show up. Assuming a 75% turnout, we therefore need a privacy booth for each 200 registered voters. As is done by the Londonderry, New Hampshire town clerk, it is a good idea to have a number of additional folding cardboard privacy screens that can be placed on tables in case more voters come.

As mentioned above, ballot marking devices that would be used by voters with disabilities will not affect the voting process for other voters. With this option, election commissioners have to determine how many disabled voters will vote in their election district and buy enough ballot marking devices to serve their disabled constituents. Commissioners should be aware that as voters with disabilities become more familiar with new voting technology, their attendance at polling sites will increase.

Acquisition Costs

A simple calculation for a pollsite with 2,000 registered voters shows how PBOS could save $45,500 in acquisition costs compared to buying DREs.

According to our figures above, this pollsite would require 10 DREs at approximately $8,000 each or $80,000.

The same pollsite could be served by a single optical scanner ($5,500) and 10 marking booths ($150 each, $1,500). It would also need ballot marking devices for the disabled.

We now calculate the number of ballot marking devices needed. Let us assume a 75% turnout (1,500 voters), that 5% of those voters (75) need special access and that each takes 30 minutes. 900 minutes divided by 30 minutes is 30. There will be a similar queuing problem for the ballot markers as there was for the DREs, so that number should probably be decreased by a factor of 2 to 15. Then the district should buy 5 ballot marking devices at about $5,500 each which comes to a total of $27,500.

Thus the total is $5,500 + $1,500 + $27,500 = $34,500 for PBOS and ballot marking device acquisition costs, $45,500 less than the figure for DREs.

Conclusions: DREs will cause long lines; PBOS can eliminate lines

The use of DREs has created long lines in many constituencies around the country. The nature of voter arrival statistics is such that there may be a large variability in the waiting times for different voting locations as governed by the mathematics of queuing theory. The only way to avoid long waiting times for voters is to have a large overcapacity, i.e. many DREs or many marking booths for use with PBOS. This is only economically possible with PBOS, as DREs ($8,000) represent the equivalent choke point in the voting process as the marking booth ($150).

DRE outages (10% in recent experience) and long voting times for persons with special needs represent further potential serious slowdowns on Election Day.

We believe that 30 minutes should be the maximum waiting time for voters. Many of them may be taking time off work, have to manage accompanying children or have medical conditions that make it difficult for them to stay at the polling place for extended times. Every precinct that follows the advice of the New York City Report to allocate one DRE for each 277 actual voters will exceed that standard. Most will have maximum wait times of at least one hour, and a significant number will have wait times greater than 1-1/2 hours.

Recent experience shows that such a result produces frustration or hardship for voters and many will leave rather than wait in long times. The analysis in the full report shows that numerous polling places allocating 1 DRE for each 277 voters will also have substantial overtimes, creating long workdays for election workers. 150 voters per DRE might work reasonably well, although the picture is clouded by DRE breakdown and use by disabled voters.

These numbers are similar to those in a story about a voting precinct with 2 DREs in Nashville, Tennessee. Elections went well with 214 voters (107 per DRE) but had long lines with 527 voters (263 per DRE).5

Some Cleveland Election Commissioners want to scrap their DREs and change to PBOS. As one election official put it, "Electronic voting systems are not scalable to meet demand on Election Day." Unlike optical scan or punch cards, where you can simply add inexpensive voting stations, there are not additional DRE (touch screen) machines available."19

The correct and smooth functioning of elections is fundamental to democracy. Everything compatible with election integrity should be done to make the process voter-friendly—overlong waits are unacceptable. If a city has hundreds of precincts and ten of them have multi-hour waiting lines or Election Day delays which force voters to continue well beyond midnight—as happened in Ohio in 2004—voters will blame election commissioners and other government officials for not having enough machines. People will leave without voting; this amounts to disenfranchisement of those voters. There will be angry charges that the election has been compromised or manipulated.

The uneven flow of voters on Election Day means that the only way to guarantee equal voter access in terms of the time it take to vote is to have a sizable overcapacity in every district. Both acquisition and operating costs make that economically prohibitive with DREs. More machines mean higher operating costs as well as higher acquisition costs. To provide for reasonable waiting times, it will be necessary to have three times as many DREs as the New York City Board of Election suggests. In contrast, it is eminently feasible to have negligible lines for PBOS systems, because it is possible to supply a large number of inexpensive privacy booths for marking ballots.


1. D Karp, T Zucco, S Nohlgren, and L LaPeter, St. Petersburg-Tampa Bay Times, "Biggest voting gripe: long lines," 2004.

2. VerifiedVoting.org, "Machine Problems Cause Long-Lines, Vote Dissatisfaction and Ultimately a New Election In Hinds County, Mississippi," 2004.

3. I Urbina, New York Times, "Officials Wary of Electronic Voting," 2006.

4. M Riess, T Wang, R Randhava, B Burt, M Schaffer, and ST Steigleder, The Century Foundation, "Voting in 2006: Have We Solved the Problems of 2004?" 10/2006, 2006.

5. B Schrade, A Paine, R Loos, and LA O'Neal, The Tennessean, "Metro wants more voting machines," 2006.

6. C Jones, ABC4 Utah, "Voters head to the polls, despite some glitches," 2006.

7. WCMH-TV, Columbus, OH, "Judge orders Cuyahoga County to keep polls open late," 2006.

8. G Kane, Recordnet.com, "Polling woes in S. J. [San Joaquin, CA)," 2006.

9. The Valley Independent, "Rage against the machines," 2006.

10. The Board of Elections in the City of New York, "An Analysis of the Number of Voters per Voting Machine", 8/21/06, 2006. [~235kb PDF]

11. Election Science Institute, "DRE Analysis for May 2006 Primary--Cuyahoga County, OH," 2006.

12. R Millman, "Do the Math," 2006.

13. M Seymour, Subject: 2004 PBOS Voting in Londonderry, New Hampshire. Personal communication to W. Edelstein, 10/2006.

14. NY State Board of Elections, "Enrollment Figures, 01-Nov-2004," 2006.

15. New York City Board of Elections, "2004 General Election, City of New York, Return of Votes," 2004.

16. AE Svizzero, New York State Board of Elections, "Authorization Testing for HAVA Plan B Ballot Marking Devices", 5/20/06, 2006.

17. American Institutes for Research, "American Institutes for Research," 2006.

18. H Stanislevic, VoteTrustUSA, "DRE Reliability: Failure by Design?" 2006.

19. J Mazzolini, Cleveland Plain Dealer, "Commissioners Want New Voting Machines," 2006.

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