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FAWS comments on How not to move the goalposts - Less Wrong
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The problem seems even worse than that. Suppose I can somehow magically determine the actual C++ ability of any weasel, and hire the first ten I come across that is above some threshold, then someone who doesn't have my magical ability would still (rationally) expect that the average skill among red weasels that I hire is lower than the average skill among blue weasels that I hire. (And I would expect this myself before I started the hiring process.) Similarly if decide to gather some fixed number of candidates and hire the top 10%.
One way Perplexed could be right is if I have the magical ability (or a near perfect test), and I decide to hire only weasels whose C++ ability is exactly X (no higher and no lower), but that seems rather unrealistic. What other situations could produce the result that Perplexed claimed?
Depends on the distribution of C++ ability. Suppose C++ weasels are a mix of normal weasels and geniuses, that geniuses have far higher ability than normal weasels, and that across both groups blue weasels are on average better by a constant considerably smaller than that difference. Your test could leave you with mostly genius red weasels and a mix of normal and genius blue weasels such that the average ability of red weasels who pass is higher.
Alternatively if far fewer red weasels learn C++ and the red weasels who do are selected for aptitude the average aptitude of red weasels who learn C++ could be higher than that of blue weasels.