NancyLebovitz comments on Open Thread, August 2010 - Less Wrong
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Since his sales rate probably increased with time, that means the average time after selling a policy is ~8 years. So the typical client of his didn't die after 8 years. Making a rough estimate of the age of the client he sells to, which would probably be 30-40, it just means that the typical client has lived to at least 48 or less, which is normal, not special.
Furthermore, people who buy life insurance self-select for being more prudent in general.
So, even ignoring the causal separations you could find, what he's told you is not very special. Though it separates him from other salesmen, the highest likelihood ratio you should put on this piece of evidence would be something like 1.05 (i.e. ~19 out of 20 salesmen could say the same thing), or not very informative, so you are only justified in making a very slight move toward his hypothesis, even under the most generous assumptions.
You could get a better estimate of his atypicality by asking more about his clients, at which point you would have identified factors that can screen off the factor of him selling a policy.
(Though in my experience, life insurance salesmen aren't very bright, and a few sentences into that explanation, you'll get the, "Oh, it's one of these people" look ...)
How'd I do?
Edit: Okay, I think I have to turn in my Bayes card for this one: I just came up with a reason why the hypothesis puts a high probability on the evidence, when in reality the evidence should have a low probability of existing. So it's more likely he doesn't have his facts right.
Maybe this is a good case to check the "But but somebody would have noticed" heuristic. If one of his clients died, would he even find out? Would the insurance company tell him? Does he regularly check up on his clients?
On the other hand, there's also selection for people who aren't expecting to live as long as the average, and this pool includes prudent people.
Anyone have information on owning life insurance and longevity?
And on yet another hand there is selection for people who are expected to live longer than the average (selection from the salemen directly or mediated by price.)