In U.S. medical school admissions, controlling for undergraduate grades and MCAT scores, the big losers from affirmative action are Asian Americans, and the winners are black and Hispanic applicants, with black applicants benefitting more.
The impact of affirmative action on white medical school applicants is very modest. The raw numbers of black and Hispanic affirmative action beneficiaries relative to total enrollments aren't huge. The number of white and Asians who suffer from it are smaller, proportionately, since those groups in the student body have larger base numbers.
The same is true at most selective undergraduate colleges and universities.
Personally, I'm ambivalent about affirmative action.
1. Affirmative action primarily involves allocation of scarce places in high prestige institutions. Almost no one is denied access to an undergraduate or law school education by affirmative action, although there are probably a meaningful number of Asian and white medical school applicants who are denied access.
2. The prestige benefits conferred on black and Hispanic applicants are very substantial and those benefits to those students almost surely outweigh any harms caused to those students by "mismatch" situations. "Mismatch" probably does have an impact on the amount of within institution informal racial segregation that occurs, however.
3. The prestige costs to white students as a whole are modest in numbers and magnitude, but those impacts are concentrated in a subset of marginal white students who tend to have less than upper middle class socioeconomic status, are disproportionately first generation college students, and tend to be cultural outsiders relative to the rest of the white student body.
4. Inadequate financial aid has negative effects on all less affluent students, and especially first generation students, that probably greatly exceed the positive benefits to those students associated with affirmative action. Less affluent white and Asian students face both financial aid and affirmative action barriers.
5. The impact on Asian Americans is quite significant in numbers and magnitude compared to white students. It rivals the negative impact on Jews a couple of generations ago.
6. Diversity is a legitimate goal and high education admissions, in general, are less meritocratic than they are perceived to be, and standard measures of academic merit are less predictive of academic and socioeconomic success in most fields than they are commonly perceived to be (this is less true in the mathematics intensive STEM fields).
7. Most people don't understand how different student bodies at highly selective higher educational institutions would look if admissions were purely made on grades and test scores.
UPDATE: A NYT Piece mentions that: "Harvard’s class of 2021 is 14.6 percent African-American, 22.2 percent Asian-American, 11.6 percent Hispanic and 2.5 percent Native American or Pacific Islander[.]" There are estimates that in an academics only regime, elite schools would be 30%-35% Asian-American, that the percentage of whites would be similar but that they would be different whites (few legacies 10-15%, fewer athletes 10% including academically weak rich kids) and that black and Hispanic admissions would fall significantly. In a pending lawsuit: "A Princeton study found that students who identify as Asian need to score 140 points higher on the SAT than whites to have the same chance of admission to private colleges . . . Harvard’s Asian-American enrollment at 18 percent in 2013, and notes very similar numbers ranging from 14 to 18 percent at other Ivy League colleges, like Brown, Columbia, Cornell, Princeton and Yale" suggest a quota. "In contrast, [the lawsuit] says, in the same year, Asian-Americans made up 34.8 percent of the student body at the University of California, Los Angeles, 32.4 percent at Berkeley and 42.5 percent at Caltech. It attributes the higher numbers in the state university system to the fact that California banned racial preferences by popular referendum in 1996, though California also has a large number of Asian-Americans."
UPDATE: A NYT Piece mentions that: "Harvard’s class of 2021 is 14.6 percent African-American, 22.2 percent Asian-American, 11.6 percent Hispanic and 2.5 percent Native American or Pacific Islander[.]" There are estimates that in an academics only regime, elite schools would be 30%-35% Asian-American, that the percentage of whites would be similar but that they would be different whites (few legacies 10-15%, fewer athletes 10% including academically weak rich kids) and that black and Hispanic admissions would fall significantly. In a pending lawsuit: "A Princeton study found that students who identify as Asian need to score 140 points higher on the SAT than whites to have the same chance of admission to private colleges . . . Harvard’s Asian-American enrollment at 18 percent in 2013, and notes very similar numbers ranging from 14 to 18 percent at other Ivy League colleges, like Brown, Columbia, Cornell, Princeton and Yale" suggest a quota. "In contrast, [the lawsuit] says, in the same year, Asian-Americans made up 34.8 percent of the student body at the University of California, Los Angeles, 32.4 percent at Berkeley and 42.5 percent at Caltech. It attributes the higher numbers in the state university system to the fact that California banned racial preferences by popular referendum in 1996, though California also has a large number of Asian-Americans."
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