I am just back from the G4G conference in Atlanta, where I gave a six-minute talk on how to organize a waiting line. The video of the actual talk will appear on the web eventually, but in the meantime, here is video of my practice run from the night before:
Or, for higher quality video, click here.
A question of practical implementation. How do you prevent a person at the back of the line from leaving the line, and then getting back into the line at the front?
An anecdote from Svetlana Alexievich I found enduringly amusing, so perhaps worth passing along, even if only slightly relevant here…. During the break-up of the Soviet Union, many people wanted to renounce their membership in the Communist Party. They wrote long letters stating their reasons why. Some became disillusioned over time, and lost faith. Others never really believed in it, but felt they needed to join the party simply to get by. They all expect to be able to turn in their membership cards along with the letters they’ve written in some sort of meaningful ceremonial exchange, to signal: I quit. But the nation is in such turmoil, there are very few remaining party members showing up for work at the office to allow that. So what happens? Long queues form, and people dutifully wait in line for hours.
I’m thinking about an actual scenario in which a basketball team has of 10 has been practicing hard, and the coach calls a break to allow them to get a drink. They are all equally parched. The coach commands that if a line forms, any newcomer to the line goes to the front.
If I were a player, and someone else raced to the fountain to get a drink ahead of me, I would probably be willing to wait behind him to take my turn. Maybe a couple of others would as well (the “Goldilocks” line). But might the rest realize that rather than wait in line, they can simply declare themselves newcomers, and go to the front? If so, who qualifies as he next newcomer? I must be missing something. Or maybe my example misses the mark because the fountain has suddenly been made available, versus the one in the park you describe.
Chad asked the same thing I did, but far more succinctly. So an explanation would be a two-for-one.
Chad and JB:
Apologies for the delay; somehow WordPress stopped sending me notifications of new comments.
You absolutely have to include (and somehow enforce) a prohibition against leaving the line and re-entering.
If that sounds impractical for water fountains, it works better for phone queues. You call Microsoft for technical assistance. A recording tells you that you’re at the front of the line but will be pushed back by each newcomer. You get periodic updates along the lines of “You are now twelfth in line”. And if you hang up and call again from the same number, your call is blocked. (Of course we still have to prevent you from using a different phone.)
An alternative is to send newcomers not to the first place, but to the next-to-last place (while prohibiting leaving and re-entering). That also achieves the optimal line length, for exactly the same reason — and makes it easier to catch cheaters, because if John is last and Chad is next-to-last, and John leaves the line and re-enters in front of Chad, I bet Chad will notice — and can employ any of the methods that we currently employ to intimidate people out of cutting into lines.
I am persuaded that from a practical point of view, it can work in some places, like the aforementioned customer call center. But if that is the case, is this truly a commonly applied queue system? If not, why not?
Question…(riffing on Gardner reference)… Five people, call them Abel, Bob, Carol, David and Ethel, are at a concert. Intermission arrives. Each is thirsty and wants a drink of water. Each want to get their drink as fast as possible, because they are really thirsty. They run to the water fountain, which utilizes the rules you mention (ie. newly arriving go to front of line). The each run at different speeds – Able is fastest, Bob a bit slower, and so forth. Some are thirstier and will spend more time at the fountain, others not so much.
Abel will get his drink first, because he was fastest and there was no line when he arrived. Who will drink second? And is their a strategy for each to maximize their chances of drinking earlier?
I haven’t read the book—so I’m still left with a number of questions.
1: Landsburg’s proposal strikes me as unjust. I suspect it would strike the other people in the line as unjust. I suspect it would strike most disinterested observers (at least WEIRD disinterested observers) as unjust. But why?
Spontaneous order: WEIRD people form queues. WEIRD people regard their position in queues as a property right. Perhaps no law or ruling affirms this view, but people hold this view nonetheless. Don’t try parking your car on the street in a space immediately after someone else shoveled out the snow—abrogation of this norm had proven fatal. “Laws are sand, customs are rock. Laws can be evaded and punishment escaped but an openly transgressed custom brings sure punishment.” Mark Twain, The Gorky Incident (1906).
2: Moreover, I don’t know how to analyze Landsburg’s proposal without engaging in intersubjective analyses without the benefit of prices/trading. Lots of people reject this kind of analysis.
So now we’re abrogating spontaneous order, rejecting property rights, and recognizing intersubjective utility. Didn’t there used to be some libertarians on this blog?
3: Now, perhaps Landsburg would put up a sign announcing the new policy, so anyone joining the queue would presumably be accepting the new terms. But I suspect the new system is sufficiently unfamiliar (and counterintuitive) as to require enforcement. Maybe enforcement would be cheap for a phone queue, but not for a drinking fountain queue. And honestly, I suspect people would complain loudly even in the context of phone queues. Coase would tell us to bear transaction costs in mind when evaluating optimal systems.
4: I know Landsburg specifies that everyone has the same utility for the water. But in real life, people don’t. And presumably the people who are willing to wait in line are people who value the water in that fountain more than the people who are unwilling to wait in line. Thus, in the absence of method for people to sell their place in line (a REAL property right), allocating water to people who are willing to wait may in fact be reasonably efficient.
5: Here’s a real queue problem: Who gets to use the available capacity on the transmission line?
Even when highways are congested, we typically allocate the next bit of space to whichever car has reached the end of the on-ramp and merges. You need to have flashing lights and a siren before you can bypass this allocation system.
But if you let too much current onto a transmission line, it can overheat, sag, make contact with something (such as a building or tree) and cause a short—or at least damage the cables. So the grid operators analyze each project that wants to connect, roughly in order of application.
They study all of the project’s consequences, internalizing its externalities. And once the operators approve the first project in the queue, they turn to analyze the next project using the assumption that the first project is already consuming its anaticipated amount of capacity. And when a study finds that the transmission grid lacks sufficient capacity for the next project, the operators announce that the project developer will first have to bear the cost of expanding the grid’s capacity.
At that point, the project developer says, “Hey, just a minute, I gotta tie my shoe. So I’ll let the next person in queue go ahead of me (and bear the cost of upgrading the grid). Once someone else has agreed to bear that cost, come back and re-analyze my project.” Naturally, you get a LOT of project developers using this same strategy to game the system—somewhat akin to a lot of people dropping out of your drinking fountain queue and the returning as a “new” person in line.
Grid operators have been struggling to come up with better systems for analyzing projects. Meanwhile, the demand for new sources of electricity keep growing and the queue keeps getting longer. Apparently the Texas grid operator (ERCOT) has developed some kind of assumption-of-the-risk model that gets projects interconnected faster, but I can’t say that I understand it.
But if you need a new project to work on, work on this one!
This scenario seems painstakingly artificial, and depends on “identical” people (but of course when you are queueing, you’d have to say “identical except for position in queue”) spontaneously materializing.
In real life, there is a crowd of people not currently in line, and with the usual queueing they would join the queue or not depending on how long it is and how thirsty they were. With the “optimal” strategy enforced, EVERY person in the crowd would join the queue and be first in line, at least very temporarily. If the rate of arrival was faster than the rate of drinking, they would make no progress unless they joined JUST when the current drinker was finishing. Effectively you are dispensing drinks at random.
If there are other fountains in the universe, this might produce some distribution of queues throughout. If this is the only fountain you are letting a lot of people die of thirst. The only currency that exists in this universe is the willingness to wait, and the proposed strategy makes that currency worthless.
Jens Fiederer (#9): “If this is the only fountain you are letting a lot of people die of thirst.”
People care about (a chance of) dying of thirst; they also care about avoiding waiting lines. The goal is to minimize either deaths or waiting lines, but to provide the tradeoff that people prefer. Under the conditions of the model, last-in-first-out achieves that tradeoff.
People also care about predicting the future, and people care about alternatives. It seems to me this model has only one fountain, no listed alternatives, and no specification for the arrival of new people. And to make things worse, you want to prohibit leaving the line and re-entering (presumably the prohibition is against re-entry, since leaving is part of the intention of your solution).
I am guessing that if you see somebody drinking, you do not join the line in the first place unless there is nobody near you and it looks like the current drinker is almost done?
Clearly if you start the line and it just keeps getting longer in front of you there does not seem to be much hope of you ever getting a drink, so starting the line is a losing move unless you can be pretty sure there is nobody else in the area. Maybe you circle the area until everybody has lined up and then you can manage to cut in front?