[Darryl_P]

I think your post describes the basics of conditional probability correctly, even if it's a bit long-winded. This conclusion, though,

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It would be more accurate to say that affirmative action redistributes opportunity from whites to blacks of similar socioeconomic positions

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is incorrect IMO precisely because of the relatively small number of situations in which your hypothetical arises.

There are much fewer blacks in that socio-economic position, so the majority of companies having to satisfy AA rules are sitting there with mostly white employees and mostly white applicants with the occasional black applicant being significantly less qualified than the whites. In order to avoid being accused of discrimination they would have to discriminate against the whites by hiring the occasional underqualified black.

So basically the dilemma you desribe about choosing between equally qualified candidates is actually a rare (and lucky) situation for an employer to be in. I say lucky because he can hire the black to satisfy AA without compromising profitability. Most employers do have to compromise on profitability to satisfy AA rules.

If I were the employer, though, and I knew I could get away with it, I would certainly hire the white guy, even if the black is slightly more qualified, and it would be for pure profit-related reasons, not anything personal against the black. The reason is that there is more trust in a homogenous environment and that fosters efficiency. Few will think the black guy will try to steal or do something drastic, but many times they won't understand where he is coming from and as an employer I won't feel like financing a Bridging Cultures 101 training course if I don't have to.