Quick, what's the top national university?

Harvard? Princeton? Instead, try the University of California in San Diego.

A set of college rankings released this week by Washington Monthly uses a different sort of metrics than, say, the more familiar kind used by U.S. News & World Report. Rather than seeking to rate universities based on reputation or difficulty of admission, the evaluators looked at how colleges and universities did based on what it considers three public goods: social mobility, commitment to research, and commitment to service.

Institutions were rewarded for things like enrolling low-income students, helping them to graduate on time, and keeping tuition low. Other factors: the percentage of graduates who go on to earn PhDs, how much work-study money is spent on service, and community service participation. Many of the results are surprising.

The rankings, which Washington Monthly has issued annually since 2005, are particularly well timed, coming a few days after President Obama launched a major initiative around college affordability and called for a new national ranking system in which federal student-aid dollars would be tied to college performance – including things like graduation rates and sticker price.

"There are schools out there who are terrific values. But there are also schools out there that have higher default rates than graduation rates. And taxpayers shouldn’t be subsidizing students to go to schools where the kids aren't graduating," Mr. Obama said in a speech last week at the University at Buffalo in New York. "We’re going to start rating colleges not just by which college is the most selective, not just by which college is the most expensive, not just by which college has the nicest facilities – you can get all of that on the existing rating systems. What we want to do is rate them on who's offering the best value so students and taxpayers get a bigger bang for their buck."

In fact, the lists that Washington Monthly released this week include rankings of the best "bang for your buck" schools – ones that combine better-than-expected graduation rates with an affordable price.

To even rank, schools had to have a student body with at least 20 percent receiving Pell Grants (offered to low-income students); have a graduation rate of at least 50 percent, meeting or exceeding the graduation rate that would be predicted based on the composition of the student body; and have a loan default rate among graduates of 10 percent or less.

Out of 1,572 colleges and universities in the broader rankings, just 349 made the bang-for-the-buck rankings. No. 1: Amherst College in Massachusetts, followed by Queens College, CUNY (City University of New York); Baruch College (CUNY) in New York; California State University in Fullerton; and the University of Florida in Gainesville.

This is a measure "that ought to be of great interest to the vast majority of students going to college but not going to the Ivy League," says Kevin Carey, director of the New America Foundation’s Education Policy Program in Washington, who was the guest editor for the rankings. "Where do I have a good chance of graduating and won’t break the bank?"

The problem with ranking systems like U.S. News's, Mr. Carey says, is that they're somewhat vague and self-reinforcing – "everyone knows that's a good school because smart people go there, and smart people go there because it's a good school" – and also irrelevant to the bulk of students, who aren't going to an elite institution.

Ranking institutions instead by their larger value to society – in terms of their commitment to social mobility, research, and service – yields far different results, he says – ones that are more useful to many Americans.

So the University of California schools, for instance, fare unusually well in the national rankings, with four of the top 10 institutions – despite the fact that in recent years California has slashed aid to state schools and they, in turn, have raised tuition. The rankings reflect the UC system's quality of research along with its commitment to enrolling low-income students, Carey says.

At UC-San Diego, 47 percent of students receive Pell Grants. At Riverside, 57 percent do. Contrast that with the prestigious Washington University in St. Louis, where just 6 percent of students get Pell Grants.

"It's the difference between elite institutions serving as an engine of social mobility as opposed to a barrier to social mobility," Carey says.

With so many weighted factors, the reasons for an institution's high (or low) ranking vary. Some that come out on top are familiar names: Stanford University in California is ranked sixth on the national list, and Harvard, in Cambridge, Mass., is eighth.

Among liberal arts colleges, Bryn Mawr in Pennsylvania comes out on top, thanks largely to its dedication to service and research. It spends more work-study money on service than any other liberal arts college. Carleton College in Northfield, Minn., which ranks second, is helped by the large number of graduates who go on to the Peace Corps and to earn PhDs. And Berea College in Kentucky, ranked third, has a staggering 93 percent of its student body receiving Pell Grants, and it boasts an impressive net price (sticker price minus average financial aid) of just $909. Berea College charges no tuition and serves first-generation college students.

Conversely, many well-regarded names are absent from the top of the list. Don't look for Yale or Brown in the top 50. George Washington University is ranked all the way down at 94, and American University in Washington at 114. Both charge high tuition, enroll few low-income students, and have lower graduation rates than statistics suggest they should.

Washington Monthly also ranks master's universities and baccalaureate colleges – institutions that accept almost all their applicants and draw from a more regional pool – and community colleges. The baccalaureate list is topped by two historically black institutions, Elizabeth City State University in North Carolina (which boasts a net price of $909) and Tuskegee University in Alabama, which comes out on top in its commitment to research.

Both schools graduate fewer than half their students (44 and 43 percent, respectively), but their graduation rate is much higher than would be expected, given the makeup of their student body.

"It's succeeding with those not likely to succeed where you add value," says Carey.

[Editor's note: The photo caption for this story was revised to correct the name of the library pictured and to clarify which college ranking system was being discussed.]