This study doesn’t just challenge one big myth about American universities and poor students. It combats several popular myths among both liberals and conservatives. Let’s go through three.

Myth #1: America’s most prestigious universities are great engines of upward mobility.

The most important takeaway from the paper is simple, and sad: The colleges that are most able to launch people to the very top of the American economic system often are the least accessible to low-income students.

Poor students who graduate from Ivy League universities (and their equivalents like Stanford, Duke, and MIT) have a much better shot at entering the top 1 percent than low-income graduates of other colleges. But these hyper-selective schools are also hyper-elite. A child from the richest 1 percent of families is 77 times more likely to attend an Ivy (or an equally selective college) than a child from a family in the poorest quintile.

It doesn’t have to be this way. Elite institutions have the capacity to double or triple their low-income access (more on that below). But even in the 21st century, most of them are essentially plutocratic.

Elite Colleges Are Truly for the Elite

The true mobility champions of higher education are the colleges that both accept lots of low-income students and send them to the upper quintile of earnings at relatively high rates. These schools are mostly mid-tier public institutions, like State University of New York at Stony Brook, where 16 percent of students are from the bottom quintile, more than four times the Ivy League average. Other all-stars in this category include California State University in Los Angeles, Pace University in New York, and South Texas College.

These schools “combine moderate success rates with high levels of access,” the researchers write. In other words, they aren’t millionaire-minters like the Ivy League. But they accept a lot of low-income students and reliably turn many of them into above-average earners.

Myth #2: Low-income students, who are more likely to be minorities, can’t succeed at selective colleges.

If the first myth is a liberal fantasy, the second is a conservative fallacy. For example, in oral arguments during the affirmative-action case Fisher v. University of Texas, former Supreme Court Justice Antonin Scalia said, “It does not benefit African­ Americans to get them into the University of Texas where they do not do well, as opposed to having them go to a less­ advanced school, a slower­-track school where they do well.”

Scalia was referring here to “mismatch theory,” a conservative critique of affirmative action, which says that minority students shouldn’t get preferential treatment at colleges, because they’ll just fail. Similar critiques have been made of affirmative action programs that seek both ethnic and economic diversity.