I must admit that I am generally not a fan of the New York Times Magazine’s The Ethicist column. Often the letters hover between whining and overly specialized or the response is too preachy but this week there was a very intriguing question (Impatience Takes a Number, Aug 26).
Returning my cable box at the Time Warner store, I arrived to find 30 people ahead of me in line. Begrudgingly, I took a number (as you do at the deli counter) and waited. A woman turned around and told me she could no longer stay. She offered me her ticket, five numbers away from being called. At first I said no — it wouldn’t be fair to everyone else who was waiting — but she insisted. I took her ticket, returned my cable box and walked out of the store while everyone else kept waiting. Was it right to take the ticket? ALEXANDRA, NEW YORK CITY
So that’s just a great discussion starter. This is not merely about line cutting, which is flat-out rude and we all know is wrong (although, as Gady has proven, it may not only be socially efficient — it can be supported in equilibrium!). The letter writer is not setting out to beat the system; she is being gifted a chance to discreetly shorten her wait.
What makes this even more interesting is that just last week, the same newspaper ran an essay emphasizing that what really matters in queuing systems is fairness (Why Waiting Is Torture, Aug 19).
Perhaps the biggest influence on our feelings about lines, though, has to do with our perception of fairness. When it comes to lines, the universally acknowledged standard is first come first served: any deviation is, to most, a mark of iniquity and can lead to violent queue rage. Last month a man was stabbed at a Maryland post office by a fellow customer who mistakenly thought he’d cut in line. Professor Larson calls these unwelcome intrusions “slips” and “skips.”
The demand for fairness extends beyond mere self-interest. Like any social system, lines are governed by an implicit set of norms that transcend the individual. A study of fans in line for U2 tickets found that people are just as upset by slips and skips that occur behind them, and thus don’t lengthen their wait, as they are by those in front of them.
So what is the right answer here?
From pure social efficiency grounds, this doesn’t matter as long as (a) everyone has the same waiting costs and (b) everyone has the same expected service time. To see the importance of the latter, note that if the customer who is bailing would have been in service for just ten seconds and the letter writer was expected to be in service for ten minutes, we know that a lot of people will be waiting when the letter writer enters service. It would be more efficient for the magic ticket to go to whomever has the shortest processing time. The difficulty here is that the customers may not know just how long it will take Time Warner to address their issue. Even if they did, there would be issues in getting them to reveal any private information on their service needs.
To see the importance of (a), consider my twelve-year-old daughter’s answer to this question: “I would give the ticket to someone who was having a hard time waiting — like a mother with small kids.” Not only does that answer make a father proud, it’s socially efficient (with some caveats about waiting times). There is, of course, an uncomfortable aspect to recognize here. The person with the highest cost of waiting might not be the mom with small kids. It could be, say, a well compensated lawyer or banker. I’m not sure my daughter would fork over the ticket to a hedge fund manager in a nice suit.
But what are the implications of handing over the ticket to someone randomly behind you in line? On the one hand, no one in the line is being made worse off relative to having the current ticket holder staying in line. But that is the wrong benchmark. The current ticket holder ain’t staying. If she were, we wouldn’t have the letter. Relative to having the current holder just leave, everyone between the current holder and the letter writer is worse off.
Some numbers are helpful here. Suppose everyone’s service will take ten minutes and that waiting in line costs each person a dollar a minute. (Remember: It’s New York and everything is expensive.) If the letter writer is jumping from being 30th in line to being fifth in line, she is saving $1/minute*24 customers*10 minutes/customers = $240. However, she has increased the waiting cost of everyone she is jumping over relative to just letting the current ticket holder leave by ten minutes. That’s a total cost of $240. (Note that anyone is position 31 and higher is unaffected.) Thus the gain of one person is equal to the loss of everyone else. The question then is whether those standing in the queue would rather be assured of saving ten minutes (which is what they would receive if the current holder just left) or have a lottery and maybe being the lucky recipient who gets a real short wait. I suspect that many would prefer the shorter wait with certainty.
Note that I am ignoring any warm fuzzy feelings that the current ticket holder would get by making one specific person feel lucky. Perhaps looking one person in the eye and making them a winner warms the cockles of her heart. And, as Woody Allen said, “nothing like hot cockles.“
As for what The Ethicist said, he came down against taking the ticket on the basis that cutting the line is cutting the line and that it is wrong to willfully game a system that is intended to make user’s life better. However, he also said something I think is wrong:
The technical answer is that the store wants to control the sequence in which customers are serviced, and that sequence is dictated by a number system. So from the store’s perspective, this is not a social contract — it’s just a rule. The store’s policy is that whoever has the next number is the next in line. If you would have walked through the front door and said, “I’ll give $1,000 to whoever gives me a number that gets me to the front of the line the fastest,” there isn’t any way you could be stopped.
Time Warner would almost certainly step into squash auctions of spots in the queue. Best Buy has, in fact, done this when people have tried to scalp positions in its Black Friday queue even though scalping would arguably lead to good outcomes. Indeed, the only people who let someone else profit from selling priority in their line may well be the TSA. Time Warner has a real interest in having its waiting room only be as crowded as it needs to be. If it allowed priorities to be auctioned, it would induce speculators to grab numbers with the hope of selling them as they approached the front of the queue. That would be most profitable when the waiting room is already crowded so service would appear to be worse than it really is. And for a cable company that is in fact saying something.