This is Part 5 of an ongoing series that started here, and you can find links to all the other posts there as well. [Update: I've restated some of this with a more careful presentation of the argument for reparations here, in Part 7 of the series. My conclusion is unaltered, but I've realized the argument for reparations had far more to be said in favor of it.]
I'm in the process of discussing the arguments in favor of affirmative action before moving on the the arguments against it, and we're up to the reparations argument now. As I summarized it in the inaugural post of the series, the argument says affirmative action is a worthy practice on the grounds that it provides compensation or reparation to underrepresented minority groups who have been harmed in the past (and perhaps still in the present) by injustices that favor the well-represented groups.
Most people I've known, upon hearing this argument, immediately object that no one today is responsible for the fact that anyone enslaved anyone else well over a hundred years ago. But the argument doesn't really assume the moral responsibility of any individual today for any actions of long-dead people. It's probably most helpful to think of this via an analogy. Suppose I grow up in a fairly wealthy family who die and leave all their money to me. I've been living a fairly comfortable life, and I haven't had to work hard to keep it that way. Then I discover something. My great-grandfather came into all this money by stealing it from another family, and I start to wonder what became of that other family. I investigate and discover that they've been living in extreme poverty since then, to the point where survival was even difficult. The last remaining member of the family is in dire straits now. I've clearly benefited greatly at the extreme expense of this last remaining family member, and it was because of a wrong that was done. I didn't do it, but isn't it at least worth considering whether I owe this person something?
How do you extend this to slavery? It seems to me that we can get a plausible moral premise for reparations by saying that, to the extent I've benefited from the existence of slavery in the past and to the extent that any have been harmed by it, I owe something to those who were harmed by it. That's the principle behind this, and it seems plausible if my conclusion in the analogy is plausible (which I think it is). What's not so clear is how to develop this specifically.