For me, the goal wouldn't be to rank the oppressed against each other, but to provide resources for all those who need it.
I think of it less like a tournament and more like food stamps: below a certain income, food becomes difficult to afford, and aid is helpful (I was on food stamps for a short bit and really appreciated it). It doesn't really matter WHY their income is low, just that society can help them with food.
College aid is similar, except that admission seats aren't as easily fungible as tuition dollars. Same for job spots, I suppose.
Let's say you have 100 openings of something. A candidate would be scored across the board, mixing demographics with performance. 10 points for an essay. -3 for bad GPA. +5 for a bad zip code. +3 for being a woman. -6 for wealthy parents. Whatever. In that way all those factors could be considered.
But yes, the exact numbers would be difficult to arrive at. Maybe we could try to statistically model those based on their impact to lifetime earnings, updated every census or whatever. It wouldn't be easy. At all.
Is it legal? I don't know. But the law can change. More to your point, I'm not even sure if this is a GOOD or ethical idea. Just a thought for discussion.