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gwern comments on True numbers and fake numbers - Less Wrong
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If it correlated better with the vast battery of non-IQ-tests which nevertheless exhibit a positive manifold, it'd be used.
Hmm, it's tricky. If new IQ tests are chosen based on correlations with many existing non-IQ tests, doesn't that also make it more likely that different IQ tests will agree with each other? And do we see more agreement in practice than we'd expect apriori, given that selection process? (I have no idea and hadn't thought of this question until now, thanks!)
Thinking about the geometry of that, it seems to me that any two things that correlate positively with all of a "vast battery of non-IQ-tests" are likely to correlate positively with each other, and the more diverse (i.e. less correlated with each other) that battery is, the tighter the constraint it places on the set of things that correlate with all of them.
Furthermore, if it correlates better with that battery than existing IQ tests do, it again seems, just from visualising the geometry, that it will correlate worse with the IQ tests than they do with each other.
But my intuition may be faulty. Do you have a concrete example of the phenomenon?
Indeed. To the extent that existing IQ tests are not terrible & crappy (and, y'know, they aren't), any better IQ test is still going to correlate heavily with the old ones.