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Yvain comments on But Somebody Would Have Noticed - Less Wrong
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One that I didn't want to include in the post because I felt it would make it too inflammatory is this reaction to a particular conspiracy theory.
If anyone's read the book "Matilda" (yes, yes, fictional evidence - I remark on plausibility only), they may remember the chillingly feasible technique of the abusive headmistress to pull stunts so outrageous that the students can't get their parents to believe them. Surely someone would have noticed if the principal of a school had picked up a girl by her pigtails and flung her.
The heuristic of dismissing things that it seems someone would have noticed probably usually works, but the things that it wouldn't work on are really big, and so I'm wary of it.
It only fails in cases where you wouldn't notice if somebody else had noticed. In a school full of terrified children, each of whom incurs a huge risk in speaking up unilaterally / going to the media about the evil headmistress, it's easy to believe that no one would have said anything. If it happened today, in the real world, I'd check www.ratemyteachers.com, where the incentives to rat on the headmistress are totally different.
The dominating principle (pun totally intended) is:
P(you heard about someone noticing|it's true) = P(you would have heard someone noticed|someone noticed) * P(someone noticed|it's true)
From there you can subtract from one to find the probability that you haven't heard about anyone noticing given that it's true, and then use Bayes' Rule to find the chance that it's true, given that you haven't heard about anyone noticing...
...I think; I don't trust my brain with any math problem longer than two steps, and I probably wrote several of those probabilities wrong. But the point is, you can do math to it, and the higher the probability that someone would have noticed if it wasn't true, and the higher the probability that you would have heard about it if someone noticed, the higher the probability that, given you haven't heard of anyone noticing it's true, it's not true.
For you to justify the rule in this post, you'd have to prove that people either systematically overestimate the chance that they'd hear of it if someone noticed, or the probability that someone would notice it if it were true.
The problem with the way a lot of people use that is that they compute P(someone noticed|it's true) using someone="anybody on earth", and P(you would have heard someone noticed|someone noticed) using someone="anyone among people they know well enough to talk about that".
Also "someone would have noticed" isn't the same thing as "someone would have noticed and talked about".