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Plane crashes
So. Inevitably after a plane crash a discussion comes up where someone may say that they're worried about flying now, and someone else pulls out the statistic that driving to the airport is more dangerous than flying. I think this reasoning is basically correct on the long-term, but not appropriate in the short-term.
Suppose it's the day after flight MH370 mysteriously disappeared. Information is extremely sketchy. You're about to get on a similar plane, operated by the same airliner, taking off from the same airport flying the same route. Should you get on the plane? That is, are you wrong to worry more than usual when we have no idea what happened to MH370? I would say no. The complete disappearance of flight MH370 without warning and without a trace the day before says **update your priors** at least for the short-term.
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Comments (9)
Your question is: after an airliner accident, how often do any of the next n flights following the same route also have an accident?
Guessing (2/3 confidence) lower than the base rate.
It wasn't "the same" route, but the 9/11 attacks have skewed the coincidence rates.
You'd expect intelligent adversaries to hit and hit again quickly, before the means of their attack were found out and countermeasures were implemented.
Close. If the accident is completely unexplained, as it often is immediately following an accident, shouldn't the risk be substantially higher immediately following the accident and then rapidly decay back to baseline as more information becomes available?
Yeah, that was my thought too - after an accident, everyone is more careful and diligent, because there will be a search for someone to blame, and that's really not a good time to be asleep at the wheel, whatever your level of responsibility.
I think you're right.
It's because we have no idea what happened that I would worry more than usual. It's not that we had no information, but that the reams of information we had wasn't adding up. Airliners are known as targets to attack by hostile agents, and a mystery disappearance seems more likely caused by an intelligent agent than unthinking causes. Intelligent agents will hit and hit again before their means of attack are found out and countered.
It is probably a beginner question here, but: it is not reasoning, it is a feeling i.e. it is the calculation done in the less-rational parts of the brain that evolved for simpler circumstances. Even if you rationally know it is not the case, you still feel worried, because one part of your brain knows it the other not and the other one is stressed. It seems then that not flying can still be a good decision just with a different justification, not "because I will crash" but "because I know I won't crash but part of me is still stressed and I would better avoid having that stress".
And this seems to be so for every irrational decision and choice... it is buying a better outcome at the cost of some less-rational part of your brain still stressing you out with worry.
I'd say that a single event like that should not affect your priors much, not enough to reconsider your travel plans. Just like you don't reconsider your driving plans after hearing about yet another car accident on the radio (unless its aftermath directly impedes your trip). However, if you learn about two or more accidents in close succession, this should give you a pause, since it challenges the model of random uncorrelated events.
Not by much, though, since there's Poisson clumping (do planes crash 2 at a time?).
That's the problem with OP: yes, in some strict sense, there will be an epsilon increase after a plane disappearing. But is this increase remotely relevant to any decision? I strongly suspect that if one attempted to formalize it, the contribution of one MH370 incident out of a century of aviation is so small it's overriden by small details of the prior or model or approximations.
Let's agree that your priors should go up slightly towards some event being behind the disaster that will lead to future flights being more risky. It's still nowhere near high enough to be significant.
How many airplane crashes were of this type? Very few, if any. So a prior on how much the prior should update should be upper-bounded by 1/number of crashes that didn't have such effects, at a crude estimate.
Or if there are some, of which you should give examples, as it would make your point clearer, then it's roughly bounded by num of crashes that led to such a situation/total num of crashes.
Plus add filtering for reference classes of crashes, e.g. how many died, other details, etc.