The last four presidents of the United States each attended a highly selective college. All nine Supreme Court justices did, too, as did the chief executives of General Electric (Dartmouth), Goldman Sachs (Harvard), Wal-Mart (Georgia Tech), Exxon Mobil (Texas) and Google (Michigan).

Like it or not, these colleges have outsize influence on American society. So their admissions policies don’t matter just to high school seniors; they’re a matter of national interest.

More than seven years ago, a 44-year-old political scientist named Anthony Marx became the president of Amherst College, in western Massachusetts, and set out to change its admissions policies. Mr. Marx argued that elite colleges were neither as good nor as meritocratic as they could be, because they mostly overlooked lower-income students.

For all of the other ways that top colleges had become diverse, their student bodies remained shockingly affluent. At the University of Michigan, more entering freshmen in 2003 came from families earning at least $200,000 a year than came from the entire bottom half of the income distribution. At some private colleges, the numbers were even more extreme.

In his 2003 inaugural address, Mr. Marx — quoting from a speech President John F. Kennedy had given at Amherst — asked, “What good is a private college unless it is serving a great national purpose?”

On Sunday, Mr. Marx presided over his final Amherst graduation. This summer, he will become head of the New York Public Library. And he can point to some impressive successes at Amherst.

More than 22 percent of students now receive federal Pell Grants (a rough approximation of how many are in the bottom half of the nation’s income distribution). In 2005, only 13 percent did. Over the same period, other elite colleges have also been doing more to recruit low- and middle-income students, and they have made some progress.

It is tempting, then, to point to all these changes and proclaim that elite higher education is at long last a meritocracy. But Mr. Marx doesn’t buy it. If anything, he worries, the progress has the potential to distract people from how troubling the situation remains.

When we spoke recently, he mentioned a Georgetown University study of the class of 2010 at the country’s 193 most selective colleges. As entering freshmen, only 15 percent of students came from the bottom half of the income distribution. Sixty-seven percent came from the highest-earning fourth of the distribution. These statistics mean that on many campuses affluent students outnumber middle-class students.

“We claim to be part of the American dream and of a system based on merit and opportunity and talent,” Mr. Marx says. “Yet if at the top places, two-thirds of the students come from the top quartile and only 5 percent come from the bottom quartile, then we are actually part of the problem of the growing economic divide rather than part of the solution.”

I think Amherst has created a model for attracting talented low- and middle-income students that other colleges can copy. It borrows, in part, from the University of California, which is by far the most economically diverse top university system in the country. But before we get to the details, I want to address a question that often comes up in this discussion:

Does more economic diversity necessarily mean lower admissions standards?

No, it does not.

The truth is that many of the most capable low- and middle-income students attend community colleges or less selective four-year colleges close to their home. Doing so makes them less likely to graduate from college at all, research has shown. Incredibly, only 44 percent of low-income high school seniors with high standardized test scores enroll in a four-year college, according to a Century Foundation report — compared with about 50 percent of high-income seniors who have average test scores.

“The extent of wasted human capital,” wrote the report’s authors, Anthony P. Carnevale and Jeff Strohl, “is phenomenal.”

This comparison understates the problem, too, because SAT scores are hardly a pure measure of merit. Well-off students often receive SAT coaching and take the test more than once, Mr. Marx notes, and top colleges reward them for doing both. Colleges also reward students for overseas travel and elaborate community service projects. “Colleges don’t recognize, in the same way, if you work at the neighborhood 7-Eleven to support your family,” he adds.

Several years ago, William Bowen, a former president of Princeton, and two other researchers found that top colleges gave no admissions advantage to low-income students, despite claims to the contrary. Children of alumni received an advantage. Minorities (except Asians) and athletes received an even bigger advantage. But all else equal, a low-income applicant was no more likely to get in than a high-income applicant with the same SAT score. It’s pretty hard to call that meritocracy.

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Amherst has shown that building a better meritocracy is possible, by doing, as Mr. Marx says, “everything we can think of.”

The effort starts with financial aid. The college has devoted more of its resources to aid, even if the dining halls don’t end up being as fancy as those at rival colleges. Outright grants have replaced most loans, not just for poor students but for middle-class ones. The college has started a scholarship for low-income foreign students, who don’t qualify for Pell Grants. And Amherst officials visit high schools they had never visited before to spread the word.

The college has also started using its transfer program mostly to admit community college students. This step may be the single easiest way for a college to become more meritocratic. It’s one reason the University of California campuses in Berkeley, Los Angeles and San Diego areso much more diverse than other top colleges.

Many community colleges have horrifically high dropout rates, but the students who succeed there are often inspiring. They include war veterans, single parents and immigrants who have managed to overcome the odds. At Amherst this year, 62 percent of transfer students came from a community college.

Finally, Mr. Marx says Amherst does put a thumb on the scale to give poor students more credit for a given SAT score. Not everyone will love that policy. “Spots at these places are precious,” he notes. But I find it tough to argue that a 1,300 score for most graduates of Phillips Exeter Academy — or most children of Amherst alumni — is as impressive as a 1,250 for someone from McDowell County, W.Va., or the South Bronx.

The result of these changes is that Amherst has a much higher share of low-income students than almost any other elite college. By itself, of course, Amherst is not big enough to influence the American economy. But its policies could affect the economy if more colleges adopted them.

The United States no longer leads the world in educational attainment, partly because so few low-income students — and surprisingly few middle-income students — graduate from four-year colleges. Getting more of these students into the best colleges would make a difference. Many higher-income students would still graduate from college, even if they went to a less elite one. A more educated population, in turn, would probably lift economic growth.

The Amherst model does cost money. And it would be difficult to maintain if Congress cuts the Pell budget, as some members have proposed. But when you add everything up, I think the model isn’t only the fairest one and the right one for the economy. It’s also the best one for the colleges themselves. Attracting the best of the best — not just the best of the affluent — and letting them learn from one another is the whole point of a place like Amherst.

“We did this for educational reasons,” Mr. Marx says. “We aim to be the most diverse college in the country — and the most selective.”