In the 2018 Midterms, some very determined Georgians waited over four hours in line to vote. Every two years there are precincts that torment voters with long lines, but never mind how or why... I'm interested in comparing the relative costs of these long lines.

Specifically the relative costs for those attempting to vote. That is, if a voter spends four hours to secure a vote, that voter has obviously spent, (or been "charged" or perhaps even "taxed" by the state), more than another voter who waited 5 minutes; the four hour voter pays 48 times as much as the five minute voter.

OTOH, that leaves out the costs of those who try to vote, but can't afford to wait four hours:

  • Let's say another Georgian can only afford to wait 1 hour, then they must go home and feed their children. Since they don't know in advance how long the wait will be, they invest the hour, and depart without voting.

  • Another can afford four hours, but at 3.5 hours they hear an estimate that the line will take 5 hours, which they can't spare, so they too depart without voting.

  • These long wait times also have a demoralizing effect, perhaps reducing turnout in future elections.

Waiting time alone doesn't seem to be a complete metric. Is there some better metric being used for situations like this that more completely assesses the costs to prospective voters and society in general?

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    An additional factor could be distance to the poll station, but that could be even more compilcated to assess (distance, public transport availability...) – SJuan76 Nov 8 '18 at 10:33

Answer: A good measure (metric) for this will have to be statistical, but simple statistics like "average wait time" turn out misleading rather than meaningful. A better metric might be the percentage of voters who have to wait longer than some specified "target" wait time . The measure can be thought of as a pass/failure rate against a quality-of-service (QOS) standard. .

Resource planning for quality improvement

I know of no way to estimate a "cost of time" to voters, but choosing a target wait time leads to a more actionable metric and planning tool. The QOS standard replaces "cost" in effect. An example a QOS standard might be that at least 80% of voters every hour wait less than 5 minutes, even during peak voting hours.

This choice is motivated by the fact it may be possible to estimate the probability of waiting longer than the target amount of time, due to a model of queuing systems in telecommunications using math first worked out by Agner Krarup Erlang. The math of predicting this it is probabilistic, non-linear and frankly a bit over my head, if you are more math inclined, see this article gives formula and definitions. For non-mathematicians, there are easy to use estimating calculators are available free online. I'll illustrate using a calculator available at https://planetcalc.com/3151/; an example and screen shot appear below.

To simplify, let's assume that the only bottleneck in voting is the number of available of voting booths. (This ignores other possible sources of delay, such as the number of poll-workers needed for checking-in voters and issuing ballots; but similar service models can be generated for each resource type used in a process.)

Lets say that at a particular polling station the peak-hour arrival rate of voters is 60/hour, and that on average it takes 5 minutes (300 s) in a booth. Given these estimates, we might want to calculate: How many voting booths would I need to meet expectations?

The math of working the answer out isn't straightforward because most voters use the booth for substantially less than 5 minute; only a few go over, but those few go way over five minutes. Also the arrival time of voters won't be spaced out evenly. Both are usually modeled as probability distributions.

But to the answer, we need to specify a quality of service goal, e.g. that 80% of voters wait no more than 5 minutes (300 s.) By plugging the four numbers into the Erlang-C calculator we can estimate the minimum number of voting booths needed at that polling station is 7. See below:

Erlang-C calculation

Any fewer voting booths is likely result in voter delays spiraling spiral out-of-control during peak hours, like the example in Georgia. The of this simplified example math works out that within limits, quality of service be improved by increasing the number of resources (like voting booths), for example to improve and achieve 95% wait times to 5 minutes, a minimum of 8 voting booths are needed.

Like any probabilistic equation, some assumptions about distributions are made. For Erlang-C applied to voting, one of these assumptions is that the voters arrive independently of each other. If instead, voters arrive by the busload every hour, the assumption is broken. For that reason, figures the calculator produces are minimum numbers, but as a metric of results(rather than planning tool) the percentage of voters who need to wait more than 5 minutes might be a good one.

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    This answer would be satisfactory if it contained a conversion formula to compute a given poll queue's efficacy (and efficiency) in Erlangs or Erlang-Bs, given specific inputs such as number of votes counted, number of line joiners, number of line leavers, et al. If it seems like there's too many variables, please use simplest cases. – agc Sep 24 '19 at 20:47
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    I see your point, I've tried to update this answer. I found a simple online calculator that might be applicable to the topic, as well as a more-complete article including factors such as line-leavers (which might correspond to "shrinkage", people who give-up due to delay.) – Burt_Harris Sep 26 '19 at 0:43
  • This answer is certainly improving, but what's still lacking is examples of the unit in action, for the purpose not of optimizing, but of measuring the utility of a line the better to compare it to other lines. That is, if the unit were fubars, we might say "Queues in Mouseville are approximately 20 fubars, versus 0.5 fubars over in Catville, so of course Felix beat Mortimer..." – agc Sep 27 '19 at 11:48
  • Note: The unit Erlang (E.) is named in honor of the engineer who created mathematical models to describe the Copenhagen telephone exchange. A pattern of voting usage that kept 1 voting booth busy for a whole hour would be considered 1 Erlang of load. This unit of measure however is more focused on equipment utilization than voter experience. – Burt_Harris Sep 27 '19 at 19:15
  • @agc, Erlangs don't have anything to do with with who beat who in the election. Instead the logic would be that if the voter turnout in Mouseville generates 10 Erlang of load (presented), but the polling place only has 7 Erlang of load handling capacity, the wait times necessarily grow over time during peak voting hours. If Catville has 5 Erlang of presented load, and 7 Erlang of load capacity, the voting delays in Catville will random and mostly acceptable. In Catville, it might be meaningful to talk about average delay, but in Mouseville average delay is meaningless and out-of-control. – Burt_Harris Sep 27 '19 at 21:01

What you propose seems quite impractical to measure at scale, i.e. interview voters about their value for the time spent. I don't know of any studies like that. I did find ballpark estimates of economic costs, which just multiply the average wage with the wait time, e.g.:

We are aware of no published analysis that attempts to place an economic value on the time that Americans spend waiting to vote. A simple way to produce a ballpark estimate is to multiply the total number of hours waiting in line by average hourly earnings. Based on an average wait time in 2012 of 13.1 minutes as reported below and an estimate that 105.2 million people voted in-person in 2012 (either on Election Day or in early voting), we calculate that voters spent a total of 23.0 million hours waiting to vote in 2012. According to the U.S. Bureau of Labor Statistics, average hourly earnings were $23.67 in November 2012. Multiplying the number of hours waiting to vote by average hourly earnings yields an economic cost estimate of $544.4 million.

We have no opinion about whether this amount is “too high,” “too low,” or “just right.” However, it is of a similar magnitude to previous estimates about the annual costs of administering elections in the U.S. For instance, in 2001 the Caltech/MIT Voting Technology Project estimated that local governments spent about $1 billion conducting and administering elections in 2000. If we combine the estimated costs borne by local governments conducting elections with the economic cost of waiting in line, a significant fraction of the economic cost of conducting a presidential election is the time spent by voters waiting in line.

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  • The height of tree might be measured in meters with a big ruler, a string on a balloon, or by it's shadow and angle of the sun, etc.. This Q. isn't asking about the method, just the "meter" itself. Think of it like a gridlocked highway with only two exits B & C miles ahead, and one entrance A miles behind. Interviews nor identities would not be necessary to measure the rates of flow -- voters take exit C, and quitters take exit B. Granted a polling place has only one exit, so we'd need to post a few line observers to count when and where quitters leave. – agc Sep 25 '19 at 16:30

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