My pre-existing United boycott, and some musing on randomness and fairness

You probably already saw the video - if not, do yourself a favor, and search for "man forcibly removed from overbooked United flight."

Other than the video evidence, which is damning, we don't have many facts, other than assertions made by various parties, repeated endlessly on social media and mainline media. Some facts, such as the United CEO claiming the passenger was "belligerent," is an assault on the meaning of the word.

United's claim that four passengers were "randomly" selected to be kicked off the flight, in order to make room for the four United employees, remains unchallenged. What procedure was used to select these four passengers, and is it really "random"?

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What does "random" mean? Mathematically, we can say that every passenger has an equal chance of being selected as one of the four. According to SeatGuru, the airplane on that route holds 70 passengers. So the chance of any specific passenger being selected is 4 out of 70 (roughly, 6 percent). This is about the same as seeing four heads in a row in four coin flips.

The seating map shows three classes of passengers, six in First Class, 16 in Economy Plus, and the rest in Economy. The first unknown is whether passengers in different cabins are treated equally or not. My hunch is that First Class passengers are excluded from this lottery. (If you know anything about this, feel free to leave a comment.) It seems to me these airlines micro-manage all decisions based on fare - for example, the fare basis is the reason why you frequently get only one or two seats to pick from when booking but when you board the plane, you discover it is half empty.

The second unknown is whether passengers within the Economy cabin were treated equally or not. As is well known, even if you sit in the same cabin, you have not paid the same fare. According to this website, the median "restricted coach" fare for this United itinerary (operated by Republic) is $219 with a range from $80 to $426. For "unrestricted coach" fare, the median is $135 ($70, $246). For "restricted first class," it lists a median fare of $102 ($67 to $469). Are lower-fare passengers more likely to get selected?

The third unknown is which passengers had connecting flights and which didn't. From an operational perspective, bumping a passenger who has a connection can create a second-order effect, as this passenger will now miss that connection. If the selection was truly random, the airlines would have ignored this factor.

The fourth unknown is how airlines handled group travellers. Given that groups of travellers are not identified by a special code (as far as I know), they can't perform random selection at the group level. Therefore, what happens might be as follows: they select randomly at the passenger level, meaning that every passenger has 4 out of 70 chance of being selected; however, if any of the randomly-selected passengers is part of a group, United personnel face one of three choices:

(a) keep the selection and break up the travelling group;
(b) disqualify the individual who is part of a group, and replace him or her with another random selection;
(c) if the travelling group is not more than four individuals, bump the whole group, which means one or more of the other randomly-selected passengers will be "relieved."

Going with choice (b) destroys the randomness because any passenger who travels in a group has zero chance of being selected. Going with choice (c) also nullifies the randomness because passengers who travel in a group have more chance of being selected - if any one group member is selected, the entire group is selected. The larger your group, the higher your chance of being bumped. Choice (a) maintains the facade of randomness but predictably, passengers in the group typically want to stay together.

For these reasons, I don't believe the selection process was truly "random." (Again, if you know something, say something.... in the comments section.)

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What would United do - in defence of randomness - if the randomly-selected passenger were a TSA "sky marshal" or, for argument's sake, Rahm Emanuel? Would they have respected the random selection?

There is a longstanding controversy amongst statisticians who use random sampling. When you are drawing randomly just one panel of people, the specific panel may be skewed. If you know that the randomly-assembled panel is skewed, do you resample?

Sometimes, random selection is not appropriate. For example, and I have mentioned this before, it is not plausible - nor is it conscionable - that the NYC police is inspecting bags "at random" in the subway system, as the announcers keep insisting to passengers. Truly random selection means inspecting only people picked out by a randomizing device. If one uses judgement to decide which bags to inspect, the process can no longer be described as "random."

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Randomness is often equated with fairness. Random is "fair" only in the average sense. But lots of events only happen once. The one instance may or may not be fair, even if randomly generated. Throwing a fair coin four times, as stated above, has a 6 percent chance of showing four consecutive heads. If you are giving out four prizes by random drawing to a room with equal numbers of men and women, and all four prizes went to the men, the process is "fair" but the outcome may be perceived to be "unfair."

The video has become a sensation in China because of the race of the passenger who was dragged along the floor like a sack of potatoes. Minorities are very sensitive to such events, for good reason.

In order to understand why minorities are quick to blame racism (or race-based bias), you have to understand two modes of thinking about uncertainty. (See also the related blog post here.)

Here is a stylized description of the "majority" perspective: You hear that the selection is random, therefore fair. You accept that claim, as you generally believe that you live in a fair and just society. You are appalled at how United treated the Asian man. You also believe that United would have bullied anyone in the same way, whether you are a massive UFC fighter, or a beautiful model straight out of the cover of Vogue. You see the incident as an aberration in a fair system.

But now flip that framing over. If you are a minority, you don't generally presume the system is fair. You know it's less than fair; you just don't know if it is a little biased, or a lot. To answer that question, you look for data. The data include incidents like this assault on the defenceless Asian man. In a Bayesian way, you update your belief system after each new incident; you think the system is a bit more unfair than you previously thought.

This line of argument is covered in this old post about inverting probability. Assume we all observe that in four coin tosses, there are four heads. The mathematician will rely on the assumption that the coin is fair, and argue that seeing four heads is highly unusual, and occurs only 6 percent of the time. The statistician will judge whether the observed outcome of four heads is sufficient evidence to show that the coin isn't fair to begin with. In other words, the direction of thinking is inverted.

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tl;dr

After the appalling incident in which an elderly, Asian passenger was forcibly dragged out of an aircraft like a sad sack of potatoes, the United management hid behind, among other things, a claim of "randomness." That claim has gone unchallenged. It is highly unlikely that the selection process was truly random, in the sense that regular people understand the word. In fact, there are many valid reasons for the selection not to be random. Statisticians have long figured out that "random" is not the elixir that solves all problems. The claim of randomness is also frequently used as a shield against allegations of bias. This incident will be seen as an aberration to those who presume we live in a fair and just society, and it will be seen, by minorities, as incremental evidence showing that the system is less than fair.

Also, to explain the title of the post: I have been boycotting United long before this appalling video. There was a time when I traveled enough to have "Premier Executive" status on United, but in recent years, I've woken up and said NO to further belittling and disgraceful treatment by sundry United personnel, including "customer service" people. #BoycottUnited

P.S. Don't let the cheap fares tempt you - it is not worth it.

P.P.S. According to the link provided by Dinesh in the Comments section, the "random selection" is a complete lie. United policy does not mandate anything like a random selection. This is the relevant text:

1. Passengers who are Qualified Individuals with Disabilities, unaccompanied minors under the age of 18 years, or minors between the ages of 5 to 15 years who use the unaccompanied minor service, will be the last to be involuntarily denied boarding if it is determined by UA that such denial would constitute a hardship.
2. 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.

The second bullet point provides a huge amount of room for discrimination.

Comments

[Dinesh]

It isn't random. I don't know why they said it was. It is governed by their IDB policy, which is part of their contract of carriage, section 25.A.2. https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec25

I've heard it said that this policy is submitted to the DOT and must be followed, but I don't know if it's true.

[Ken]

One reason for not kicking off First Class passengers is that the compensation paid is based on a multiple of the fare paid, so it is obviously cheapest to boot the lowest payers. In this case it was going to be expensive as the next flight was the following day, so their were hotel bills as well as compensation, and if I paid the ridiculous amount for first class I would be unhappy if they gave me a cheap hotel.

That actually leads to what they should do. Make a lower cost fare that has no guarantee of that flight, and make it clear at booking. Limit it to about 5% or 10% of passengers and then those passengers can't complain because they have chosen that fare. At the moment they are trying to hide the fact that they actually do this. I always fly a reasonable time before anything important because this, as well as weather and other circumstances delay flights.

[Z]

"If you are giving out four prizes by random drawing to a room with equal numbers of men and women, and all four prizes went to the men, the process is "fair" but the outcome may be perceived to be "unfair.""

Seems like you could always find some dimension along which the winners were all from the same group. I think fairness is a property of the process and not the outcome.

[Kaiser]

Z: you got the crux of the post. In textbooks, we like to start with the assumption of a fair process and compute the chance of an unlikely outcome. But the reverse problem is even more interesting. Usually we observe the outcome and we do not know how it is generated. In this case someone asserts that the process is fair but it is not auditable. So reasonable people can interpret the unlikely outcome either as a chance rare event of a fair process or an average event of an unfair process.