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IlyaShpitser comments on Open Thread, January 4-10, 2016 - Less Wrong Discussion
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https://en.wikipedia.org/wiki/Central_limit_theorem
That is the case that +ing amongs many should be gaussian. If the distribution is too narrow to be caussian it tells against the "+ing" theory. Someone who is amadant that it is just a very narrow caussian could never be proven conclusively wrong. However it places restraints on how ranodm the factors can be. At some point the claim of regularity will become implausible. If you have something that claims that throwing a fair dice will always come up with the same number there is an error lurking about.
The variance of the Gaussian you get isn't arbitrary and related to the variance of variables being combined. So unless you expect people picking folks out of a lineup to be mostly noise-free, a very narrow Gaussian would imply a violation of assumptions of CLT.
This Jewish law thing is sort of an informal law version of how frequentist hypothesis testing works: assume everything is fine (null) and see how surprised we are. If very surprised, reject assumption that everything is fine.
Thus our knowledge on people being noisy means the mean is illdefined instead of inaccurate.
Sorry, what?
having unanimous tesitimony means that the gaussian is too narrow to be the results of noisy testimonies. So either they gave absolutely accurate testimonies or they did something else than testify. Having them all agree raises more doubt on that everyone was trying to deliver justice than their ability to deliver it. If a jury answers a "guilty or not guilty" verdict with "banana" it sure ain't a result of a valid justice process. Too certasin results are effectively as good as "banana" verdicts. If our assumtions about the process hold they should not happen.