Paper: Overbooking flights

In recent news (cn: autoplay), a United Airlines passenger was unwillingly dragged off a plane to make seats for employees. The incident was partially blamed on the common practice of airlines to deliberately overbook flights in order to make up for all the no-show passengers.

While I won’t discuss the particulars of this incident, I am willing to do something that most journalists are not: read relevant academic literature. I just picked one paper that appeared to have a sufficiently broad perspective:

Marvin Rothstein, (1985) OR Forum – OR and the Airline Overbooking Problem. Operations Research 33(2):237-248.

The basic problem is that many people who buy airplane tickets don’t show up. In 1961, the Civil Aeronautics Board (CAB) reported that 1 out of 11 ticket sales were no-shows. These numbers are about the same today, with 7-8% no-shows. The airlines could create wait lists to fill the empty seats, but it would be impossible to contact the wait-listed customers in a timely fashion unless they were already present at the gate.

The solution has been to deliberately overbook flights based on statistical predictions of the number of no-shows. Marvin Rothstein says that airlines have been deliberately overbooking at least as far back as 1960 when he first started working in the airline industry. Note that this is well before the US Airline Deregulation Act, which passed in 1978. The regulating board, CAB, approved of overbooking practices, stating that “present reservation systems of the carriers greatly benefit the traveling public”.

Since overbooking relies on statistical predictions, there will occasionally be cases where the predictions are wrong, and there are too many no-shows–or too few. When too many people show up to be seated, then the airline has to “bump” people off the flight. The CAB reported that from 1963-1964, there was about 1 bump for every 1,300 boarded passengers.

Bump rates are around the same today, but there’s a crucial difference.  Today, we distinguish between voluntary and involuntary bumps, with about 90% of bumps being voluntary.  In the 1960s, AFAICT they didn’t bother asking for volunteers, so basically all bumps were involuntary.

A chart showing the number of voluntary and involuntary bumps for various airlines from 2008-2016. Most major American airlines, including United and Southwest have around 1 voluntary bump per 1,000 passengers, and 1 involuntary bump per 10,000 passengers. Virgin America and Hawaiian, have hardly any bumps, while JetBlue has zero bumps.

From The Economist. The vertical axis shows voluntary bumps per 100,000 passenters, and the horizontal axis shows involuntary bumps.  The airlines in the lower left corner are very conservative about overbooking, and JetBlue doesn’t overbook at all. Note that Delta has relatively few involuntary bumps–I’ll talk about this later.

In 1961, the CAB tried to address the problem by instituting a no-show penalty. No-shows would have to pay 50% of the ticket price (which I think means they can only be refunded 50%, not that they pay an extra 50%). But they ended the no-show penalty in 1963 because they felt it was bad for public relations, and it was difficult to distinguish passengers who were no-shows because of connecting flight delays.

In 1968, industry outsider Julian Simon proposed a solution to the overbooking problem: when too many people show up, hold a sealed auction to find who is most willing to be bumped. Every airline rejected his idea at the time.  Simon published some amusing responses from the airlines:

United’s other objection is that “such a procedure would raise serious doubts in our customers’ minds concerning our ability to maintain even a reasonably efficient reservation scheme,” i.e., passengers might think that United overbooks intentionally – as it does.

Overbooking practices were kept in obscurity until 1972, when Ralph Nader himself was bumped from a flight. He filed a suit, and the Supreme Court ruled in his favor in 1976. In response, CAB made overbooking practices more transparent, increased the penalty that airlines pay for bumping passengers, and instituted the practice of asking for volunteers before bumping people unwillingly.

At this point, airlines found they could pay less by paying passengers directly, rather than paying the CAB penalty. Thus many airlines tried auction-like practices. Practices vary from airline to airline, but usually they hold a fixed-price auction.  They have an agent explain the situation and offer compensation for passengers to leave the airplane.

Very few airlines actually use the sealed auction originally proposed by Simon. A notable exception today is Delta Airlines, at least since 2011. From the above chart, you can see Delta has fewer involuntary bumps than other major airlines. The problem with the sealed auction is that it’s likely that the winners of the auction suffer from winner’s curse (ie they won the auction because of poor value estimation).

So if you don’t like United Airline’s overbooking practices, you could instead choose Delta or JetBlue.  However, I suspect most people will continue to prioritize ticket prices.

I close out with a quote from Marvin Rothstein, in 1985:

The passengers are supposedly on notice that the airlines overbook, but one wonders to what extent they really understand what is taking place. How much longer will the present precarious balance last? Probably only until someone brings another landmark lawsuit that upsets the whole applecart.


  1. Jessie Harban says

    The basic problem is that many people who buy airplane tickets don’t show up. In 1961, the Civil Aeronautics Board (CAB) reported that 1 out of 11 ticket sales were no-shows. These numbers are about the same today, with 7-8% no-shows. The airlines could create wait lists to fill the empty seats, but it would be impossible to contact the wait-listed customers in a timely fashion unless they were already present at the gate.

    It should be noted that (with few exceptions), no-show passengers do not actually receive a refund on their tickets. Those 1 in 11 seats may be empty, but they’ve still been paid for and still technically belong to the people who didn’t show.

    So this is a “problem” only in the sense that airlines feel entitled to get paid twice for 7-8% of the seats they sell.

  2. says

    Right, a lot of airlines today have the no-show penalty that CAB instated from 1961-1963. This allows airlines to have lower list prices, although the true price isn’t really any lower because customers incur the risk of losing their money.

  3. Kwt says

    The EU rules about this are very sensible. If you deny boarding, it is the airline’s responsibility to get you to the destination by rerouting. Any delays in reaching the final destination (subject to a minimum) result in a bonus cash compensation to the passenger depending on distance of original flight. Passengers are additionally entitled to meals, accommodation and care.

    The great thing about this is that it’s a set of rules every airline is obliged to follow, so there’s no confusion. If the airline doesn’t pay up, send your case to a company with receipts and they will for a cut of the compensation, hound that company until it pays.

  4. polishsalami says

    One factor that should be taken into account is where this person was.

    I’d say that passenger that had boarded the plane and was seated is reasonably entitled to fly (except for such things as the pilot having a medical episode, bomb threats, etc). This passenger had ‘passed the point of no return’.

  5. says

    I’m not sure that’s any different from airlines in the US. If they bump you, I think they will also compensate you and reroute you. And all the rules about bumping are, in principle, public knowledge.

    Yes, my impression is that most involuntary bumps involve denying people at the gate, rather than removing passengers from the cabin. Removing people from the cabin is clearly worse if it involves police.

  6. embraceyourinnercrone says

    As the incident happened because the airline wanted those 4 seats for a flight crew that they need to get to Louisville the overbooking rules possibly don’t really apply ( they were booting paying customers to make room for their employees basically).

    But as was earlier mentioned in the comments here, the seat has been sold whether or not anyone shows up to occupy it. So how is it legal to sell the same goods or services to two people at the same time?? Why should the passengers have to participate in an f’dd up version of The Lottery for the privileged of being able to use an airline seat they ALREADY paid for?

    Removing someone from a seat they paid and showed up on time to use sounds like assault and battery and interfering with someone having use of a service they paid for. That the police did it doesn’t make it right.

  7. says

    Well, you don’t have to participate in a lottery. You can put your money where your mouth is and patronize airlines that don’t overbook.

    The ~8% no-show rate suggests that if prices are fair, you’d be paying an extra 8% in order to avoid a 0.01% risk of being involuntarily bumped. Your mileage may vary but personally I’m not willing to pay that. I think there’s a problem where customers are not fully informed of overbooking practices, but being fully informed I would still buy tickets from airlines that do it.

  8. anothersara says

    As mentioned above, the recent incident *was not caused by overbooking*. There were enough seats for all customers with reserved confirmed seats who showed up. The bump was to seat employees, not customers, which is different from bumps due to overbooking, and thus overbooking rules do not apply, and overbooking policies are irrelevant, or at least not as relevant as many other things which much of the media is ignoring, such as contract violation, or whether the Chicago Department of Aviation has the authority to interfere at all since their job is to enforce airport rules, which the passenger did not violate. See this blog post for more on why this distinction is important:

    As for the topic of overbooking, some airline markets do use waitlists instead of overbooking. For example, flights to/from the Matsu archipelago (in the East China Sea) are never overbooked, and the airline maintains waiting lists for passengers who want to have a chance to buy tickets for sold out flights. This system works because demand is always greater than supply (the government imposes price controls on the airfare), and it is not feasible to increase supply. 40-90% of all flights to/from Matsu are canceled due to weather (the percentage varies by season), or the airplanes have to turn around midflight and go somewhere else because it’s too dangerous to land in Matsu, which means there are always people willing to hang around the airports to try to grab a seat at the last minute. This is an unusual situation.

  9. says

    Whenever some well-publicized incident occurs, the public generally ignores how atypical the incident is, and searches for some similar set of events that are much more common. So when some guy gets kicked off a plane (a highly atypical incident), some people ignore the details and instead talk about overbooking, which affects hundreds of thousands of people a year. So yeah, that’s what I did.

    But I agree that this particular incident didn’t actually involve overbooking. And further, even if you think overbooking is acceptable, that doesn’t mean you must find the incident acceptable, or vice versa.

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