OR/MS Today - December 2007|
Minimizing Voting Queues
The Right Not to Wait
Forecasting and simulation show promise in reducing waiting times to vote.
By Douglas A. Samuelson, Theodore T. Allen and Mikhail Bernshteyn
A group of O.R. analysts has developed a promising solution to the problem of long waiting lines at polling places. The solution includes improved forecasts of how long people will take to vote, taking the number of offices and issues on the ballot into account, and simulation of different proposed allocations of voting machines to precincts. The results, tested in a few counties in 2006, indicate that improved allocation of machines to precincts, producing much better voter service, can be achieved at minimal cost. The results also indicate, however, that the acquisition of new touch-screen voting machines, in response to the Help America Vote Act (HAVA), may make the problem worse in many instances because of the increased time required to vote using these machines.
The company, Sagata, Ltd., of Columbus, Ohio, markets this solution as a software package, Sagata VotePro. Outputs include expected waiting times at the worst precincts, expected latest precinct closing times and average overall waiting times. The software can show the expected performance of a given voting equipment allocation or indicate a recommended new allocation based on specified goals.
Simulation is necessary for several reasons:
It appears that people generally underestimate how difficult it can be to achieve that all voters wait no more than a specified threshold. For example, New York State has recently introduced a rule that no voter should wait more than 30 minutes before casting a vote. The more voters there are within a jurisdiction that wants to satisfy this goal, the more difficult it is to achieve the goal. The cause of this is what some probability modelers, especially in reliability, call "multiplicity" the way that the probability of at least one undesirable outcomes grows with the number of independent "trials," Assume, for instance, that one precinct has a chance of 1 percent of having a voter who would experience a wait longer than 30 minutes. Then, if the precincts are probabilistically independent, a county with 200 precincts would face a chance of 1-(1-0.01)200 = 0.86 of having at least one precinct where there would be a voter waiting longer than 30 minutes.
This effect, in turn, implies a larger than expected "safety stock" of machines is needed to avert having even one precinct with long waits, taking unexpected events into account. For demonstration purposes, assume a one-minute average voting time and a 70 percent voter turnout for a county with approximately 200 precincts each servicing about 1,200 people. The relationship between the number of machines and the expected average waiting time looks like Figure 1.
However, a seemingly good average waiting time of, say, four minutes, in the Figure 1 plot would translate for some (few) voters into waits of about two hours in the plot shown in Figure 2, which shows the expected waiting time for the precinct with the longest waiting time. This suggests that the New York State requirement that no voter wait for more than 30 minutes is more difficult to achieve than acceptable wait on average.
Also, these plots indicate the consequences of allocating an insufficient number of machines, as was the case in the well-publicized Ohio presidential election in 2004. The performance deteriorates quickly as the number of machines decreases, both in terms of the average waiting time across all vote centers and waiting times at the "worst" precinct.
An additional complication is that, if machine allocation is done in a fair scientific way, it is generally impossible to know ahead of time which precinct is going to be the "worst." The nature of randomness will lead to a few vote centers being less "lucky" in terms of voter arrival pattern throughout the day, voter age/literacy, etc.
Figure 3, a typical output from the program, indicates that some locations will experience average waiting times in excess of 30 minutes. The program also produces more detailed results, showing maximum waits in addition to the precinct averages shown, which in this case predicted that some voters might wait in excess of five hours.
Studies in Ohio in 2006
In 2006, Franklin County commissioned Election Science Institute (ESI), which in turn included Sagata in its team, to conduct "what if" analyses and generate recommendations about how to avoid the waiting time problems the county experienced in 2004. This study concluded that a one-minute increase in how long it takes to vote from 5.7 to 6.7 minutes would shift Franklin County from minimal to long waits. Such a shift could occur, for example, because of extra ballot items or poor voter instruction, for example. The study also predicted that certain precincts, mainly in the Gahanna area, would have relatively long waits, and additional resources (if any) should be transferred to these precincts. The county official in charge said that he would use that information to put additional absentee ballots in Gahanna but would not shift the allocation. For 2008, state officials are currently considering using simulation for allocation.
Actual experience in the general election in November 2006 bore out the model's predictions. Again, although the county had purchased many more machines, there were long waits in a few polling places because the allocation was insufficiently tuned to account for variations in how long people took to vote. This is a function of the length of the ballot, the complexity of some of the issues, whether voters have studied the ballot ahead of time, the structure of the voting process and how quickly voters assimilate the information.
An unexpected and unfortunate characteristic of some of the new machines is that they tend to require more time for most voters to get through the ballot. Rather than seeing the whole ballot at once, as on older lever-pull machines, voters are guided through one office or issue at a time. Also, when a voter skips an office or question, the machine prompts to make sure the non-vote was intentional. This feature apparently causes many voters to pause and reflect, substantially increasing the average time voters spend casting their votes.
Also in 2006, Sagata, InfoLogix and a number of other service providers, again as part of an ESI effort, conducted a thorough assessment of how well the new DRE touch-screen voting machines performed in Cuyahoga County (Cincinnati), Ohio. The results raised concerns about a number of issues, including the increased time some voters needed to use the machines, the difficulty of auditing results, and the vulnerability of the machines to both errors in use and deliberate tampering.
A more recent study in New York State also pointed out the potential problem of longer voting times offsetting the benefits of acquiring new voting machines. Officials in at least one major county are accustomed to voters requiring less than 30 seconds to vote once they are at the "open-face" lever machines they still use. When we told them that we had data from direct recording equipment (DRE) machines that require the user to scroll through multiple pages in Franklin, Ohio, with average voting times longer than seven minutes, they were amazed. They were also very worried because with larger numbers of the more expensive DRE machines being required, they would exceed their budgets. In general, if average voting times increase tenfold, one could easily need to acquire ten times as many machines as the jurisdiction had before just to duplicate the waiting time performance experienced previously. The county officials were particularly interested in the implications of simulations relating to the specific machines to be purchased since previous studies had indicated variations in average voting times. In fact, even linearly proportionate increases in numbers of machines might not suffice, as greater average voting times also tend to have greater variation, and it is the longest times, not the average, that determine the severity of the resulting problem.
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