In a follow-up to the story earlier this week about outgoing Amherst President Anthony Marx’s efforts to increase the number of low-income students at his school, David Leonhardt wonders in the New York Times about next steps:

How can top colleges be persuaded to admit more talented low- and middle-income students? The first potential lever is the federal government. It pays for and administers Pell Grants, a huge program that benefits, roughly, the bottom half of the income distribution. I’ve argued that Pell Grants and other federal aid should be tied to graduation rates, with colleges at risk of losing financing if their graduation rates (adjusted for their student population) are too low. Perhaps students should also be at risk of losing financing, if they do not stay on track to graduate, as is the case in West Virginia.

But the government isn’t the only lever. Foundations can make a difference, too.

This is awfully optimistic.

In the last five years, the Century Foundation’s Richard Kahlenberg writes, the proportion of Pell recipients (which is generally taken as proxy for the amount of low-income students at a college) at more than 60 percent of America’s richest colleges in fact declined. This is despite extensive rhetoric about increasing diversity and financial aid to offer education to America’s brightest and poorest students.

The trouble is that the solutions Leonhardt proposes might be a good way of increasing access to many of America’s colleges, but it probably wouldn’t do much to move America’s most elite schools. That’s because his solutions address only the finances of college, not the supply and demand of the admission process.

Elite colleges don’t actually want to be that much more economically diverse. In fact, once an institution gets beyond that 20-25 percent of students receiving Pell Grants, Americans cease to see these colleges as elite; they become merely “good.”

Because college in America is so expensive, and often funded by parents, the whole concept of a rigorous college education is weirdly tied up with notions of class and the privilege of the aristocracy. Rich people go to elite colleges. Graduating from an elite school, therefore, offers the promise that one might get to become a rich person. That’s what we think elite colleges are.

Putting too many low income students (or too few rich ones), no matter how smart or hard working, into the school makes it less exclusive and less attractive for applicants. That’s something colleges desperately want to avoid.

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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