Here's a quick news quiz: Who said, "Fully funded vouchers would relieve parents from the terrible choice of leaving their kids in lousy schools or bankrupting themselves to escape those schools"?

If you guessed Secretary of Education Betsy DeVos, you're wrong. The correct answer is Sen. Elizabeth Warren (D., Mass.).

Drawn from a 2003 book that Warren wrote with her daughter, the quote has been making the rounds on right-wing websites. Warren supported vouchers, and now she is flaying DeVos for doing the same! What a hypocrite!

For their part, liberals maintained an embarrassed silence about Warren's comment. Vouchers have become a "dirty word" in the left-wing lexicon, as Warren lamented in her 2003 book.

But Warren and DeVos actually represent different strands of the voucher movement, which used to attract liberals and conservatives alike. So let's pause to consider whether there might be some room for compromise.

The intellectual forefather of vouchers was conservative University of Chicago economist Milton Friedman, whose 1955 essay on "The Role of Government in Public Education" argued that public schools had become inefficient monopolies. But if every kid received a voucher, which could be used at any private school as well as public ones, the schools would have an incentive to innovate and improve.

The idea was picked up by left-wing thinkers like Jonathan Kozol and Christopher Jencks in the 1960s and 1970s, but with a twist: Vouchers should be distributed progressively, with the poorest kids getting the biggest share. That way, disadvantaged students would be able to attend expensive schools that were typically reserved for the rich.

Jencks wrote a report on vouchers in 1970 for Republican President Richard Nixon, illustrating the bipartisan spirit around the idea. He proposed giving poor kids vouchers worth twice as much as middle-class students received. Jencks' plan also required participating schools to accept low-income kids' vouchers as full payment, providing another leg up for kids who had been left behind.

But the sails went out of the left-wing voucher movement in the late 1970s, when the rising Christian Right seized upon vouchers as a way to subsidize parochial schools. Among those activists was DeVos, whose family plowed millions into several failed school-voucher referenda in Michigan.

Significantly, these voucher plans did away with the idea of distributing vouchers progressively. In the last Michigan vote on vouchers, in 2000, each student would have received about $3,300 to attend the school of her or his choice.

Likewise, in the voucher plans that currently operate in 14 states and the District of Columbia, every participant gets the same amount of money. And it doesn't buy a whole lot in the educational market, where the best schools cost many times more than the typical voucher provides.

So we shouldn't be surprised that most contemporary voucher plans haven't improved student achievement, either. A recent Brookings Institution study of programs in Indiana and Louisiana found that students who used vouchers to attend private schools scored lower on reading and math tests than did similar students in public schools.

That's why Warren's 2003 voucher proposal used the term fully funded. Under her plan, students would receive a voucher "that paid the entire cost of educating a child," not just a portion of it. That would allow students to attend any public school in their school district.

Unlike Jencks' 1970 report, Warren's plan exempted private schools from the menu of student choices. But the overall goal was similar: provide poor students with vouchers large enough to let them attend the same quality schools that rich kids do.

That's probably not what President Trump had in mind on the campaign trail, when he proposed a $20 billion voucher plan to assist America's poorest students. But perhaps there's an opportunity for a bargain here. What if liberals and conservatives agreed to a few pilot programs, on the condition that poor kids got vouchers big enough to let them study anywhere? Liberals would have to put aside their reflexive antipathy to vouchers, while conservatives would need to dispense with the fiction that an equal (and paltry) payment to all students can possibly yield equality between them.

There would be other issues to work out, especially the tricky question of public dollars for religious schools. But we can get past those, too, if we're truly committed to educational fairness. Both parties insist that a student's future shouldn't be determined by her or his zip code. Let's see if they have the courage to do something about it.

Jonathan Zimmerman teaches education and history at the University of Pennsylvania. He is the author of "Campus Politics: What Everyone Needs to Know" (Oxford University Press)