because admission is a binary decision, when considering a particular case, either race tipped the scale or it didn’t (when you change the race the admission decision changes or it doesn’t). That is why O’Connor is being incoherent when saying race can play a role but it cannot be a determinative factor – for a binary decision any factor that plays a role will be determinative some of the time.

Kinsley is, I think, assuming that all the applicants are somehow linearly ranked, a cutoff point is determined (based on desired class size, perhaps), those above the cutoff point are admitted and those below rejected. He then considers the last few applicants admitted and compares them against the applicants immediately below the cutoff point. If different consideration of race would have caused any or all these people to switch places, then their admission was determined by their race. If not, not.

Healy (and Drezner and probably O’Connor) visualize admissions officers reading an application and marking it “A”, “D” or “?”, without much reference to other applications. Their thought processes are not easily reducible to rule nor amenable to counterfactuals. A different officer reading the same application may mark it differently (in a fair number of cases does, which is why admissions processes need some way of resolving such disagreements). The same officer reading particularly a marginal application at a different time, in a different mood, in a different state of digestion, might have marked it differently. The question, Would the decision change if the race changed? is unanswerable.

It may be true that “for a binary decision any factor that plays a role will be determinative some of the time” but it is not necessarily true that we can recover which factor was determinative in any particular case.

And it’s probably worth emphasising that the actual admission mechanism in Gratz looked more like the model I’m speculating is in Kinsley’s head and the actual admission mechanism in Grutter looked more like the model I’m speculating is in Healy’s. Which may be why the decisions came down the way they did.

So Kinsley’s way of thinking (from the presepective of the applicant) really doesn’t add a lot fo value.

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Being black is an insufficient but necessary condition for “being a person who would not have got in based on SAT scores but does so after extra points are awarded to black people”, and being a PWWNHGIBOSSBDSAEPAATBP is an unnecessary but sufficient condition for being awarded a place. So it is permissible under the ordinary language meaning of “cause” to say that being black caused some PWWNHGIBOSSBDSAEPAATBP to get into university.