I did not make any assumption quantifying how much worse it is. It need only be marginally worse.
Sorry, I was assuming a utility function that summed over the amount of suffering each person experienced. You seem to be using a Rawls-style utility function base on minimizing the suffering of the worst of individual. (BTW, that's a very stupid function to use in anything outside a very simple toy model.
No. I can construct similar counterexamples where there are two observable properties (which you can think of as black/white, male/female), corresponding to four populations (black males, ..., white females).
Only by fiddling with the parameters very precisely.
If your assumption is that people whose expected intelligence is bellow the median (or really the nth percentile for any n) will be treated as dumb, the only way a counter-example like yours can work is by having lots of people exactly tied for the nth percentile. And the more other information is available the more the numbers in the scenario must be jiggered for that to happen.
You will need to make your assumptions more explicit if you want to rule out these kinds of counterexamples.
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...
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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