Sorry, I was assuming a utility function that summed over the amount of suffering each person experienced.
Your claim was that more correlates means fewer false positives. This is an abstract mathematical claim about epistemic probability. Utility functions don't enter into it, at least not explicitly. It's a claim about some class of probability distributions and criteria for categorization ("positives"). I'm just trying to figure out what class of distributions and criteria you're talking about.
My counterexamples show that your claim doesn't apply in full generality. You now claim that such counterexamples require "fiddling with the parameters very precisely." I take this to be the claim that all scenarios satisfy your claim, except for some measure-zero subset (with respect to some natural measure). Can you prove this?
the only way a counter-example like yours can work is by having lots of people exactly tied for the nth percentile.
I'm not sure how to make sense of this. It doesn't seem to reflect an understanding of my example.
I argued in the continuous limit. A measure-zero subset of people are tied for exactly the nth percentile. Recall that I said that "the proportion of individuals with intelligence between a and b is b − a." So, the proportion of people whose intelligence is exactly tied for any value x is x − x = 0.
Of course, the continuous limit is only an approximation of the discrete reality. But I can find discrete examples where this proportion is arbitrarily small. It's never "lots" relative to the size of the entire population, if that population is of any significant size.
I meant lots of people tied for the nth percentile in terms of your estimate of their intelligence, which was happening in your scenarios because the amount of information available was discrete and very small.
Today's post, Why Are Individual IQ Differences OK? was originally published on 26 October 2007. A summary (taken from the LW wiki):
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