I’ve heard (in conversation) that distributions of human abilities (such as IQ) have fat tails compared to normal distributions, so +7 SD would be more common than 1 in 10^12. I haven’t found a good reference for this yet… if anyone else has one I’d like to see it.
Not an answer to your question, but according to this, at most about 1 in 200 people are at least at +7 SD if the distribution is unimodal and symmetric (unimodal for the theorem to apply, symmetric so you can divide by 2). 200 seems like a uselessly low number, so I’m now regretting having pointed people at that theorem previously. :-)
ETA: though, even the useless 1 in 200 bound seems like an unrealistically high level of reasoning ability for priests.
I thought of that, but decided that the OP wasn’t taking it into account, and so the error was worth pointing out (which turned out to be correct). On the other hand, I don’t see how one can establish a linear scale of ability. IQ measure, for example, is often defined based on calibration in a form “1 in X”, and then giving, say, 16 points above/below 100 for each standard deviation to the area in normal distribution weighting 1/X. This also allows to cross-check IQ tests with other g-factor tests, competitions, etc.
I’ve heard (in conversation) that distributions of human abilities (such as IQ) have fat tails compared to normal distributions, so +7 SD would be more common than 1 in 10^12. I haven’t found a good reference for this yet… if anyone else has one I’d like to see it.
Not an answer to your question, but according to this, at most about 1 in 200 people are at least at +7 SD if the distribution is unimodal and symmetric (unimodal for the theorem to apply, symmetric so you can divide by 2). 200 seems like a uselessly low number, so I’m now regretting having pointed people at that theorem previously. :-)
ETA: though, even the useless 1 in 200 bound seems like an unrealistically high level of reasoning ability for priests.
I thought of that, but decided that the OP wasn’t taking it into account, and so the error was worth pointing out (which turned out to be correct). On the other hand, I don’t see how one can establish a linear scale of ability. IQ measure, for example, is often defined based on calibration in a form “1 in X”, and then giving, say, 16 points above/below 100 for each standard deviation to the area in normal distribution weighting 1/X. This also allows to cross-check IQ tests with other g-factor tests, competitions, etc.