One of the odd things about college admissions and public policy is how truly unalike admissions and financial aid problems are from one institution to another. Most colleges aren’t that selective at all. The average acceptance rate at four-year colleges is about 66 percent. Community colleges, which about 44 percent of all American undergraduates attend, are all open admission.

A certain small number of colleges, however, those we often write about, let in very, very few students, and no one seems much to worry about cost. Those who don’t get in, and many allies, find this situation deeply unfair, and try to find ways to “fix” the problem.

Dylan Matthews writes in The Harvard Crimson that it’s time to dramatically change college admissions. Well, at Harvard anyway:

Chad Adelman… has proposed adopting the system used to match medical residents to hospitals. High school seniors would apply to a single admissions body and list their school preferences in order. Schools would set a minimum SAT score and high school GPA so that they do not admit students who truly cannot handle the work, but, otherwise, schools are randomly matched with students who list them as a preference.

Harvard… should set its own minimum threshold and then randomly cull from that vast majority of applicants who meet it. William R. Fitzsimmons ’67, Harvard’s long-time dean of admissions and financial aid, has said that 80 to 90 percent of Harvard applicants are qualified to be here. Harvard should identify that 80 to 90 percent, and then randomly accept 1600-1700 of them.

Matthews has hit on something kind of important in elite college admissions. The reality is that there are so few slots available for education at America’ fanciest colleges that many, many people are denied admission at schools for which they are very much qualified to attend.

It’s true that the current system might keep out the lazy and the stupid, but it utterly fails to admit those who are capable. Meritocracy after all, is not just about keeping unqualified people out; it’s abut letting the qualified in. Selection based on merit is only a fair and effective means social sorting if there are more or less enough enough slots available for everyone qualified. When the system is so structurally misaligned that there isn’t enough room for the best people it can’t really be called “fair” anymore. Universities (Harvard and the other 10 or so schools like it) begin to admit and reject people for essentially capricious reasons.

So there is a problem, but would the lottery improve anything? In fact it appears the Matthews solution is essentially useless. It would work only if all universities bought into the lottery plan.

And that simply won’t happen. Colleges and universities want to be able to select students on their own, and build a class made up of a nice mixture of ethnic minorities, athletes, legacies, and rich people (all very smart of course).

Harvard also might be able to take one or two classes using a lottery but over time this would kind of degrade Harvard. The school doesn’t want to admit just people “capable” of succeeding; it wants to be able to admit a whole bunch of scary brilliant kids, and also build a football team, and also admit many students with parents rich as Croesus so it can keep building new buildings and offering full scholarships to kids from Harlem with perfect SAT scores.

Because let’s be honest, it’s the collection of the exceptionally good students that makes Americans think the school is superior, rather than merely very good.

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Daniel Luzer is the news editor at Governing Magazine and former web editor of the Washington Monthly. Find him on Twitter: @Daniel_Luzer