Thought experiment: if you made all admission decisions by lottery, by randomly admitting a previously decided, fixed number of n applicants out of all valid ap

Thought experiment: if you made all admission decisions by lottery, by randomly admitting a previously decided, fixed number of n applicants out of all valid applications received, and the resulting cohort of admitted individuals was later found to significantly differ in demographic composition from both the local and nationwide composition of population, would that be discriminatory? If not, would it at least be problematic? What if it differed significantly from the demographic composition of the pool of all valid applications received? This case is very unfortunate, because it literally pits racial categories against one another, and claims that Asian-Americans are being unfairly disadvantaged by affirmative action applied to Hispanic and Black applicants, whose likelihood of successful admittance is proportionally much higher, in part due to their race. What's unusual is Asian-Americans apply to Harvard at much higher rates that they occur in the population, which complicates the math, and encourages some reflection about the roles of affirmative action, e.g. whether it intends to counterbalance a pipeline shortfall, or improve absolute outcomes among groups whose society-wide outcomes have lagged behind, or to right past wrongs. These are questions worth asking among ourselves when we see that in some cases, and when faced with the allocation of a limited number of a resource (a chance for a Harvard education) to a large group of people. It's hard to avoid thinking that this may be an edge case of affirmative action that was purpose-selected by this group to force the courts to consider a larger issue.