My return trip from Lubbock to Rochester took almost 36 hours, due to maintenance issues on three separate aircraft. This leads me to wonder whether American Airlines is erring too far in the direction of safety and too little in the direction of getting people where they want to go — perhaps even recklessly so.
Here’s what the back of my envelope shows:
First, a standard ballpark figure for the value of a life is about ten million dollars. What this means is that empirically, people are willing to pay about $1 to avoid a one-in-ten-million chance of death, about $2 to avoid a one-in-five-million chance of death, about $10 to avoid a one-in-one-million chance of death, and so on for various other small probabilities. (Theory tells us that willingness-to-pay to avoid a probability of death should be some constant times that probability, as long as the probabilities are small. Data tell us that the constant is somewhere around ten million dollars.)
Next, I’ve noticed that when airplanes are overbooked and people are offered $600 to give up their seats, there are very few takers. That suggests that for most fliers, getting to their destinations on time is worth more than $600.
Next, 10 million divided by 600 is a little under 17,000. The value-of-life calculation suggests, then, that people are willing to pay no more than about $600 to avoid a one-in-17,000 chance of death.
(The above is arguably iffy, since you might argue that 1 in 17,000 does not count as a small probability. With a little effort, I’m sure one could dig up some data indicating the size of any necessary correction.)
Put that together, and you’ll find that a flight should be canceled only when it has a greater than one-in-17,000 chance of crashing. If the risk is any lower than that, then people would rather take that risk than lose $600, and would rather lose $600 than wait for the next flight — so we can infer that they would rather take the risk than be delayed.
The actual risk of crashing in a U.S. domestic flight seems to be somewhere around one in seven million. Seven million divided by 17,000 is a little over 400. That means that a flight should be canceled only when the plane appears to be 1/400 as safe (i.e. 400 times more likely to crash) as the average plane in the sky.
(I’ve assumed here that all flights are fatal to all passengers, whereas in fact it seems that well over half the passengers survive an average plane crash. But I’m going to bias this calculation in American’s favor by assuming that surviving a plane crash is roughly as bad as dying in one.)
I am happy to believe that some planes in some circumstances are more than 400 times as dangerous as the average plane. I am skeptical that three planes, all of which I was booked on over a single two-day period, all met that criterion.
If I’m right about that, then American Airlines is way too safety-conscious. And I missed teaching my classes for no good reason.
It’s not just the time of the people booked to take that flight, though. If Airline X has an airplane crash, the bad publicity from that event may reduce future sales. I’m not sure how to amend your calculation to take that into account, but it seems fair that it should be taken into account.
Good analysis. One correction: A number can’t be 400 times less than another positive number without being negative. So your phrase “400 times less safe” should read “1/400th as safe.”
The real answer is that American is having a dispute with their mechanics union (over doing some major maintenance in overseas locations). So the mechanics are writing up tons of minor issues and delaying aircraft until management gives in to their demands.
But I understand what you were trying to do with your analysis.
David R Henderson (#2): Fixed, and thanks.
Steve S (#3): I was unaware of this. Thanks for the insight.
American Airlines has virtually nothing to do with it. As a practicing pilot, I can assure you that all of the decisions were made by the FAA. The mechanics, and I am sure that part is also true, were taking advantage of a miasma of pusillanimity imposed from above on the aviation industry.
Reflecting on Steve S (#3), I wonder how much of this is in American’s control. It sounds like their hands are tied once a mechanic writes something up, presumably because of regulation. I have no reason to expect government bureaucrats to get the relevant calculations right or even have an incentive to do so. Again, the safety point is well-taken, but the real culprit may not be American.
Steve S (#3), I read about this happening a few years ago with American and their pilot’s union:
https://slate.com/business/2012/10/don-t-fly-american-airlines-conflict-with-pilot-s-union-is-destroying-american-airlines-service-quality-and-you-have-to-stay-away.html
The pilots couldn’t go on a normal strike so they just started following safety regulations so scrupulously that it paralyzed the airline.
I wonder if it’s a coincidence or if this happens a lot to American Airlines specifically for some reason.
Patrick M (#1) it seems like this weighs on both sides of the equation though, because being on time ought to get good publicity (airlines get rated based on the percent of their flights that arrive on time).
Whether customers lose their time or lose their lives, those costs are born by the customers — but both can result in negative publicity which hurts American.
There is one thing that weighs on only one side of the equation though, which is lawsuits — you can’t sue American if your flight is late, but they could be sued if the plane crashes and there is a paper trail showing that there were known issues.
Prof. Landsburg,
Good analysis.
As I’m sure you know, people being unwilling to give up their seats and take the next flight for $600 is not quite the same thing as them being willing to pay $600 to get to their destination on time, or avoid an approx. 1-in-17,000 chance of death however, because of the endowment effect.
I don’t think this alters the overall conclusion of your argument, especially given you’ve made some other rather conservative assumptions, but is probably worth acknowledging.
If peoples willingness to pay to keep their seat was, say, approximately half this value (i.e. $300), the flight still shouldn’t be cancelled unless the chance of crashing is approx. 200 times more likely than average.
It’s still incredibly unlikely that three planes, all of which you were booked on over a single two-day period, all met that criterion.
@Ally,
intuitively, I think you are correct that the endowment effect plays a big role in this case.
I also think SL failed to take into account one more problem:
Because people don’t fly only one time in their lives, but many times, the “not small probability” issue is probably more important than allowed for.
If you are a frequent business traveler – or a member of a flight crew, for that matter – then you will generally be much less inclined to take on additional risks on a regular basis.
The value of the probability of life is on the margin, but it is not clear that we should not consider what one would be willing to pay for 50% to 100% reduction in chance of losing ones life in a year.
I ask this question if a person earns $4,000,000 over a life time and must/does spend much of this on elements not related to preserving her/his life, how can the market price of life be an order of magnitude greater than the available resources the individual has to spend on it.
The small marginal slice approach values the margin but does not value the full life.
@Advo #11
So (in my head at least) Steve’s back of the envelope calculation doesn’t actually apply to the “average person” so much as the “average flyer”. I think that takes into account the fact that you’re quite likely to run into a frequent flyers, who’re dealing with repeat risks? On the other hand maybe it makes the 1/17000 figure wrong?
“My return trip from Lubbock to Rochester took almost 36 hours, due to maintenance issues on three separate aircraft.”
Steve, you take the airline’s explanation at face value. Air travel is an industry built on lying to its customers. Maybe there was a maintenance issue, but it is equally possible or more likely that the delays resulted from deliberate business decisions. Airlines frequently cancel or delay under-booked flights to consolidate them with the next scheduled flight, yet explain it as a maintenance issue. The habit of lying is so engrained in airlines that they do it even if there is no apparent reason, like claiming that a flight is delayed by 30 minutes when they already know that it will be at least one hour. A worthwhile research project would be to answer “Why do airlines lie so much to their customers?”
Yeah, it turns out that people are weird and inconsistent. Some people drive because they are afraid of train crashes and use minor roads because they see pictures of freeway pileups on the news.
Air travel is incredibly safe and I am sure people are more sensitive to safety in aviation than other means of travel. It may be because they feel helpless – if driving you may feel in control even if this is an illusion. So I am not surprised at the direction of the calculation. The magnitude does seem surprisingly large.
If we assume that all airlines implemented your policy, we could presumably expect 400 times the number of crashes. I would not be too surprised to find this would pout air travel in the same bracket as road safety, so maybe not so surprising after all.
SL: “a standard ballpark figure for the value of a life is about ten million dollars. What this means is that empirically, people are willing to pay about $1 to avoid a one-in-ten-million chance of death, about $2 to avoid a one-in-five-million chance of death…”
Does that jibe with inferences from life insurance policies? ‘value of life’ must surely be known in the industry.
Would the analysis differ for ‘frequent flyers’?, say those who fly once or twice or more a week? I would think they would pay a higher price to avoid a fatal crash.
Regardless, an interesting post.
This is looking at things from the consumer’s point of view, but AA is not in the business of maximizing consumers’ surplus, but it’s own bottom line and they probably perceive that a fatal crash will cost them more in profits than 10,000,000*Number of passengers or, more likely, want to be perceived as appearing to believe it. Please check with Robin Hansen for details
#18. This was what I was getting at with my earlier comment. i don’t think AA (or airlines in general) are being too cautious, I think the travelling public are inconsistent and require greater caution from airlines than is indicated by other indicators of risk.
One plane crash is news for weeks, thousands killed on the roads is not news at all.
Fear is not a rational response to risk. There are possibly two factors – people perceive the risk to be greater and they fear same risk more than for other activities.
Rebes 14 – I automatically triple whatever delay estimate they give. I can only assume they believe we prefer getting bad news in small doses; in economic terms maybe it’s a play on loss aversion? The total disutility is less if each time resets the “origin”. (Just trying to be charitable as this blog encourages :))
Oh man that’s awful Steve! Your tale pushed me over the edge to share my artwork more widely.
Steve, perhaps you’ve underestimated the cost of a crash. Others have already pointed out the business losses to AA, but there’s more: A high-profile crash reduces public confidence in flying, which reduces flying. Less flying plausibly means (a) higher transactions costs spread over the entire country (and perhaps more), and (b) more driving, which is deadlier per mile than flying.
I’m not sure whether these add up to something that makes the whole back-of-envelope hang together, but I’d imagine they are substantial.