New Thread On Sklansky Extrapolation Question

[TomCowley]

I didn't think that normal-ish was the only possible distribution. Double-humps are plausible if there is one iffy piece of evidence that has two plausible evaluations, one of which ends up with a price of "about 70%", and the other "about 40%". Everybody is pretty confident that one of these two answers is correct, but is only slightly confident in their own answer- my specific objection was to large double-humped groups with high confidence.

Once you postulate wacky distributions, you're basically assuming the extrapolation isn't valid, which isn't necessarily wrong, but it's not an interesting result. I wanted to start with the friendliest assumptions to see if the extrapolation worked in those circumstances, so I could see what conditions were necessary to make it true, but it didn't work even then.

That being said, if the trend is 5% up to 30% with increasing IQ (yes/no skill), then I think it's safe to rate Y a higher probability to be true than if the trend is 30% down to 5%. That's also justifiable by simply giving smarter people more weight and not extrapolating. I'm not sure about the 5%-30% trend case compared to other cases that end up at 30% (flat 30%, decreasing to 30%, etc). As much "intuitive" sense as it makes to extend the line, if I want to set a price without knowing anything specific about Y, I have yet to come up with any justification for putting the probability of Y being true far away from 30% in any of those cases.

I'm also not convinced that it's even meaningful to discuss a price here, since this has a lot of similarity to the bent coin/personal probability stuff (that I really don't want to rehash), but if I had to set a price to prop-bet somebody with the same information, I haven't yet found a justification for it being far away from 30% (possibly a little different based on some form of weighted averaging across the groups, but not based on extrapolation).