the real standard is orthogonal to your cutoff-with-lottery versus rank-by-test-scores.

The real standard was that 'disparate impact' of the black pass rate being less than 80% of the white pass rate was prima facie evidence of discrimination; the more recent cases suggest that any statistically significant difference can be evidence of discrimination. If you ever got the impression that I didn't think that was how the courts behaved, I apologize for the miscommunication on my end. (I left out the four-fifths part, and just mentioned 'over 90%', because I thought it would be more communicative than adding the additional detail.)

I still maintain that if you are seeking to promote, say, 5% of the population, no merit-based test which gives you the top 5% of the population will pass the four-fifths rule in the presence of underlying racial differences in merit. (This would be the 'rank-by-test-scores' approach.) Promoting from the entire pool at random would not discriminate by race, but it also wouldn't discriminate by merit. The way to both have some merit selection, and not run afoul of the four-fifths rule, is to set some cutoff such that the rate at which blacks are above the cutoff is at least 80% of the rate at which whites are above the cutoff, declare everyone above that cutoff as having passed, and then promote randomly from those who passed.

It's still not clear to me what you think you've disproven, or why you think you've disproven it. How long this conversation has gone and the propensity for others to downvote your comments suggest to me that it may be wise to call this conversation done here, or move it to PMs if you're interested in carrying on.

I've lost about 150 karma (and the actual loss if it wasn't for people voting up -1 comments would probably be more like 250). The moderators have done squat, if we even have anything that passes for moderators. (The admins, then.)