Only 19 percent of the seats in the U.S. Congress are held by women, despite the fact that women make up more than half the United States’ population. Congress being what it is these days—a snarling ragebeast incapable of compromise—it’s an easy jump to wonder if this wild gender imbalance might be part of the problem.

Take it from Senator Susan Collins, a Republican from Maine. “I think if we were in charge of the Senate and of the administration that we would have a budget deal by now,” she told ABC News in 2011, surrounded by her fellow female senators. “What I find is, with all due deference to our male colleagues, that women's styles tend to be more collaborative.”

Are women more willing to compromise?  It’s a question that defies a simple answer, with studies that flip back and forth—women are more cooperative! Wait, they’re not!—on what seems like an annual basis. The most recent entry, released earlier this month, is a National Bureau of Economic Research working paper that focused on how gender affects bipartisanship. It concluded that women are indeed more likely to cooperate across party lines, but only if they’re Republican, and particularly if they’re working on a bill that focuses on health, education, or social welfare. In short, collaboration tends to happen only under very specific circumstances.

“I think there is sometimes the claim going around that having more women would promote diversity and maybe also improve team outcomes, because women are better able to build bridges,” said M. Daniele Paserman, an economics professor at Boston University and one of the authors of the study. “Within this sample, there’s really not that much showing clear differences between women and men. That could give some pause to the thought that increasing the number of women will have all these great improvements.”

Paserman’s study, written with Stefano Gagliarducci of the University of Rome Tor Vergata, examined 20 years of congressional data, ending in 2008, to count how often female legislators successfully rallied co-sponsors to their proposed bills. The more sponsors from the opposite party, the more bipartisan the legislation.

That Republican women held the edge over Democrats in collaboration might be surprising, given the current logjam in the Republican-controlled Congress (and the fact that female Democratic legislators outnumber their Republican counterparts three to one). But the authors argue this is caused by the fact that women tend to occupy the leftward wing of their respective parties. For moderate Republican women, Paserman said, that opens up room for cooperation with centrist Democrats. More progressive Democratic women might be less willing to turn back toward the center for collaboration on legislation, however.

From the paper:

Female Republicans’ policy positions are closer to those of the median voter, and they are more likely to sponsor bills that attract bipartisan support; by contrast, female Democrats’ positions are more distant from the median voter. On the other hand, we find no support for the hypothesis that women are inherently more willing to compromise, as that would imply that women in both parties would attract more bipartisan support, in contrast to what we observe in the data.

Granted, this doesn’t jibe with what most people believe, or what female politicians say. More than a third of Americans think women are better at working out compromises in government; only 9 percent believe men are better. And collaboration is just one part of good governance. For years, academics have investigated whether women are more effective political leaders in general, with sometimes surprising results.

For instance, are women better at getting their legislation passed into law? A few years ago, a study published in the American Journal of Political Science found that women lawmakers are more effective in pushing bills through committees—but only if they’re in the minority party. Once their party takes control of the House, their advantage against men disappears, said the University of Virginia professor Craig Volden, the paper’s author. He theorized that unlike male legislators, women often refuse to grandstand and gum up the works when they’re in the minority; the relative paucity of women in leadership positions likely also plays a role.

Even more interesting is one of Volden’s latest papers, which examines how often female legislators are able to advance their priorities. Tallying up legislation on education, health, and housing—issues on which women introduce legislation more frequently than men—he found that women are less likely to see those reforms become law than if a man had advanced an equivalent proposal. “Not only are ‘women’s issues’ brushed aside in Congress, but they’re particularly brushed aside if sponsored by women,” Volden said. “I could imagine that being enormously frustrating.”

What drives these differences between women and men in Congress? This, too, has been hard to pin down. In the NBER paper, Paserman tried to account for each congresswoman’s personal biography and the demographics of her district, eliminating as many factors as possible to nail down the essential differences between men and women.

He admits there are unknown variables. A popular theory posits that since women face a higher barrier to entering politics—in many parts of the country, voters have never elected a woman to Congress—the legislators who fight their way through are more competent and capable than their male counterparts. There’s also a fraught notion that women are biologically more conciliatory, a conclusion that seems rather paternalistic and unmoored from fact.

Kelly Dittmar, a scholar at the Center for American Women and Politics and a political science professor at Rutgers, has reached a conclusion that is also backed by conversations with women in Congress: Women, far more than men, prize results over status. In an oft-cited 2001 survey of American members of Congress, the number one reason to run for office, according to female legislators, is the ability to effect change in society. The number one reason for men? They always wanted to be a politician.

“Women just want to get things done,” Dittmar said. “They’re not in it for the show.”

Dittmar believes Washington’s ineffectiveness has made running for office less appealing to women—they’re reluctant to go through the meat grinder of campaigning if they won’t be able to get anything done. And the academic literature offers some support to that notion. If Republican women have traditionally fared better than Democrats at finding across-the-aisle cosponsors, but are stymied at the committee level when their party is in power, what leverage do they hold in today’s Republican-controlled, hyper-partisan Congress? And if women are consistently more progressive than the men in their party, how will female GOP legislators fend off primary challengers as the party moves right?

These questions haunt Erin Loos Cutraro, the co-founder and CEO of She Should Run, an advocacy group that promotes women’s leadership in government. While there are now more Democratic women serving in the House than ever before, Republicans have seen a decrease in female representation since a peak in 2007.

“You can look at the numbers and see there are fewer Republican women stepping up,” Cutraro said. “As we see increasing polarization within the political parties, we’re going to see less and less friendly territory for Republican women to first be encouraged to run, and then get the support they need to make it through a primary.” The same forces that could aid liberals like Elizabeth Warren might make it impossible for members like Olympia Snowe to get elected.

So can women fix Congress? If every man in the Capitol were replaced with a woman, we couldn’t say for certain that more bills would be passed, or that party divisions would disappear. We can’t even study it effectively; all existing scholarship about women in government is based on a legislature that has always been dominated by men. At the very least, the data suggests Congress might shift to the left on social programs and education.

More concretely, it appears that women are more willing to work with their rivals to get things done—when they’re empowered to do so. But right now, they’re not being given the chance. The Democrats will be fine; as the array of congresswomen lined behind Nancy Pelosi during her speech at the DNC last month shows, there’s no shortage of talent interested in running for seats in the Democratic Party.

It’s the Republicans who have to worry about recruitment. And if women continue to opt out of the Grand Old Party, conservatives won’t be the only ones feeling pain. It could make bipartisanship even harder to attain, and a functional government ever more distant.