Silvia, this is a very nice analysis!
I do have a quibble with one part: you notice that arbitrariness goes up when you ignore race. This does not really show that considering race reduces it. This really shows (I suspect) that ANY systematic reduction in sample size will reduce arbitrariness, but not really an argument for it.
Still, in thinking thru your analysis I wonder if the national policy should be more nuanced:
First schools must partition students into a pool of candidates on the basis of merit w/o any consideration of race. This selected pool should be indistinguishable (or maybe nearly indistinguishable) on the basis of merit.
- THEN race and other secondary factors (like parents at school, donations to school, race etc) are allowed to be considered to break ties.
Schools would need to justify that the cutoffs for the top pool are so high that the remaining candidates are truly INDISTINGUISHABLE in practical terms.
But once this determination was made then race biasing could happen w/o loss of merit.
I wonder if such a law could be made practical?
It would be a novel way to thread thru this issue.
(of course some will still view the lower chances for a white candidate in the top pool to be unfair, but at least it is not an unfairness that is lowering standards. Thus one has removed on of the two major objections.)
Interestingly, I personally have tended to be skeptical of race as a selection criteria, so i am helping to further the "other" side here. But I guess my objection has mostly been about the merit side of the equation. Also splitting in this way would show in mathematical ways just how much of a "headwind" race based selection was making in the process. So as a white male we could artificially adjust down the number of race based selections to match the non-race based selections and thus show mathematically what percent reduction "unfairness" happened to the non-race based selections.
E. g. we could see: "Oh, the inclusion of race made it 20% harder for non-race based selectors to get in." being able to show numerically might make it easier to swallow since it contains it instead of allowing folks to believe that it massively reduces chances.
