It’s time for some game theory, United Airlines edition

I agree the man should have left the plane in the first place, the police should not have used violence, the CEO should have apologized right away, United (possibly) should have known earlier it needed to transport the employees, and a bunch of other things.  Perhaps United should have mimicked Ryan Air and charged people fifteen euros (or much more!) for dragging them off the flight.  But let’s put that behind us and consider some analysis:

United policy says:

The priority of all other confirmed passengers may be determined based on a passenger’s fare class, itinerary, status of frequent flyer program membership, and the time in which the passenger presents him/herself for check-in without advanced seat assignment.”

There is also an exception for disabilities.

From the passenger’s point of view, this operates like randomization, as customers were told “the computer will decide.”  An alternative of course is to eliminate the random shuffle and require cash payments to passengers no matter what, waiting until someone volunteers to give up his or her seat at the required high price.

One problem with using money to buy people out of queues is that it encourages more upfront queuing to begin with, and that involves negative externalities for passengers as a whole.  In any model of stochastic demand and fixed capacity in the short run, demand will sometimes be too high, and I don’t know of many retail markets that rely on price alone to ration quantity.  Given that reality, I am not sure why everyone is insisting the airlines should do things this way.  If Nordstrom starts to run out of their blue cooking pots on the day of the sale, so be it, they don’t raise the price toward the end of the day as supplies dwindle.  Paying $5 to each denied pot-buyer just ensures they are more likely to run out of pots the next time around.

You could spend many moons debating whether price-only solutions to short-run shortages lead to higher or lower upfront prices (and thus higher or lower deadweight loss) than price + quality adjustment solutions to short-run shortages.  As far as I know, this question hasn’t been settled, and quality adjustment is well-known as a means of enabling more upfront price discrimination.  If nothing else, it pushes more people into business class.  The subtler mechanism is that the airlines have plenty of reasons to favor their more loyal customers, if only because of market segmentation, and this is one of them.  The market segmentation effects brings more collusion, and higher prices, but the price discrimination effect tends to boost output.

To consider possible analogies, let’s say it was a queue to buy concert tickets, with more people in line than seats for the show.  One option is to give cash to those who can’t get tickets, rather than just turning them away, but I’ve never heard anyone argue this would be efficient.  The cash payments are a tax on product supply and also they encourage too much queuing in the first place.  Instead we send some people home without tickets, even if they have waited in line for a long time.  In essence, randomization is one factor behind who is sent home without a ticket, because no arrival, when deciding whether or not to show up, knows exactly how many other people will have been prior in line.  Don’t be surprised if the airlines sometimes use a similar system.

As Garett Jones points out, sometimes the ATM runs out of cash and you don’t get any bonus afterwards.  There are plenty of other examples.

Maybe United should allow for a secondary market for the doctor to stay on the plane by buying flying rights from some other passenger, one who wouldn’t take the United offer but who might take the doctor’s better offer.  That idea is worth consideration, though arranging the contract could be tricky unless the passengers belong to a common system with pre-arranged arbitration in place (Facebook could run it?  PayPal?)  With tickets this kind of resale works smoothly through StubHub and the like.  (By the way, once the guy proclaimed he was a doctor going to see his ailing patients, did any of the other passengers offer to get off instead?  Hmm…)

The “re-accommodation” seems much worse to many people because the doctor already was seated.  An endowment effect argument therefore might require that the airline use a full auction once seats are taken.  That would increase the incentive of the airline to spot demand-supply imbalances in advance of boarding, and it might well be a good idea.  On the other hand, the presence of an endowment effect can help make “removal” an especially effective pre-emptive demand tax in world-states of potential excess demand.  The more you hate being removed from your seat, the fewer people have to be removed to achieve a greater S-D balancing ex ante.  Furthermore, the highest valuation buyers will make sure to be loyal buyers, which presumably is what the airline wants.

The cynical, who have studied randomization in optimal tax theory (that is not I, I love human rights too much and spent my youth reading the Salamancans), would even say that the higher value are the trips, and the more people fear being manhandled, the more it makes sense to use stochastic pain as a deterrent for overbooking.  Think of it as a way to increase the degree of ex ante price discrimination, and limit cross-buyer externalities, at minimal cost in terms of actual output.

Finally, the United episode gets at a more general problem with algorithms.  Even if the selection of seat loser is “truly random,” it will not always look random to the outside world.  The bumping of the doctor has been a huge event on Chinese social media, and how many of those Chinese are thinking that the doctor was bumped because he was Chinese.  The international loss of reputation here is significant, and it damages the United States as a whole, not just United as a brand name.  In essence, individual companies under-invest in perceptions of fairness, and reliance on “truly random” algorithms can make this worse rather than better.  A deliberate human chooser might well have done better, if only by knowing that a public defense of the choice would have been required, and that might have nudged United back toward the full auction or some other solution.  In essence, companies may be oversupplying “reliance on randomness,” not taking the collective negative externality into account.  Counterintuitively, relying on algorithms can increase perceptions of unfairness, and many of the costs of unfairness come on the perceptions side, even if “the true model” is making choices using a fair process.

Two other factors are worth considering.  First, due to social media it will be increasingly difficult to write and enforce retail contracts with legal meanings very different from their “common sense” meanings.  Maybe I’ll write a separate post on whether that will raise or lower transactions costs, but I suspect a bit of both.

Second, given that the stock of United tanked after the incident, now airline customer service will improve rather rapidly.  In the long run of course that will translate into higher prices too, so the net effect of this shift will prove regressive.  The more you complain, the more you are redistributing wealth — through the medium of preferred price-quality configurations — away from lower earners and toward the wealthy.

I’m not saying that the United rules are efficient, either generally or in this particular case, but I do see many people not even willing to ask the question of under what conditions they might be efficient.  And that is indeed to correct way to start on analyzing this problem.

Addendum: This is also a story of price controls, on that let’s turn the microphone over to Air Genius Gary Leff:

More importantly, United didn’t do it because Department of Transportation regulations set maximum required compensation for involuntary denied boarding (in this case 4 times the passenger’s fare paid up to a maximum of $1350). So they’re not going to offer more than that for voluntary denied boardings, especially since the violent outcome here wasn’t expected and the United Express gate agent had no authority to do more.


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