Best metric for comparing poll queue times?

Question

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?

Answer 1

In telecommunications (telephone systems), the measure of queueing is the Erlang.

I've never seen it used in the context you are interested in, but as it's a dimensionless unit that measures variable utilization of a fixed capacity service.

Trying to imagine it in a voting context, I think you would (over a period of time like 1 hour) measure the arrival rate of voters and the average time they spend using a resource (e.g. using a voting station) and multiply them to get the Erlang based measurement. In telecommunications these measures are easy to automate, but voting might be more complex, but certainly not impossible..

There are specific related measures such as Erlang-B that address other factors such as probability of being blocked on arrival.

The unit is named in honor of Agner Krarup Erlang who created mathematical models to describe the Copenhagen telephone exchange. This field is called queuing theory.

Note that there is also a programming language by the same name. As far as I know this is a different matter, but both are used in telecommunications.