> You immediately assume one of the three is the brightest of them, because your understanding of Affirmative Action Policies says this particular race has the highest likelihood of having higher overall test scores.
I think it's important to distinguish between probabilities and possibilities. It is possible that any of them has the highest score. However, it is most likely that the Asian does.
Let me articulate this phenomenon in a more neutral example. Suppose you start an elite academy for the game Go. All of the best Go players in the world come from places like South Korea, China, etc, who have a long history of playing the game. However, you would like to increase the appeal of the game internationally, so you institute an affirmative action policy that says 50% of your students must come from non-asian countries.
Let's say you have 100 slots to fill each year, and you operationalize your affirmative action policy as follows: You take all the asian applicants, rank them by ability, and take the top 50. You take all the non-asian applicants, rank them by ability and take the top 50.
It should be obvious that, in this example, the average absolute ability level of the two groups will be quite different. The incoming Asian group would crush the non-Asian group in competition. This isn't due to any innate racial capacity gap, but due to the historical and cultural relationship to the game of Go.
Now, you educate each group together for say, 4 years. That education process may homogenize ability a little bit - helping the lower performers improve more than the higher performers (though the opposite may also be true), but it's probably not sufficient to close the rather large incoming skill gap.
Now, if you were watching a match, and the only things you knew about the two competitors were that they both attended your elite academy, and one was from South Korea, and the other was from California, who would you bet on to win?
It's entirely possible that the Californian is better! It's just less likely, given no additional information. Critically, this isn't an argument against the affirmative action policy. The AA policy is doing just what it should do - helping to close the skill gap. But it does means that statistical reasoning about racism has to be sensitive to this confounding variable if it wants to make truly accurate inferences.