So far, Elizabeth Warren’s Democratic primary strategy seems to be working pretty well. She’s been steadily gaining support since the spring, when she was polling around fifth place, and is now neck-and-neck with Bernie Sanders, according to RealClearPolitics’ polling average. Early-state activists think she’s gaining momentum, the most plugged-in subset of Democrats seems to be coalescing behind her, and she’s well-liked among primary voters. But she’s still not within striking distance of Joe Biden, who continues to hold a double-digit lead over the rest of the field.

Of course, that could change if Warren convinced a significant chunk of Democratic women voters to join her coalition. Women make up about 60 percent of Democratic primary voters and typically turn out at higher rates than men, and with only five women left in the race, Warren is carving out a space for herself on gender issues. She has announced ambitious plans to protect abortion rights, narrow the pay gap for women of color, establish universal child care and combat maternal mortality. And although Warren has struggled so far to gain support among black and Hispanic voters, she’s pitched many of her policies on gender specifically to women of color.

But is it realistic to expect Warren to win over women in the primary? A study by CBS News and YouGov conducted earlier this year found that Democratic women were much more likely to prioritize female candidates in a series of hypothetical matchups, but it turns out there’s very little evidence that women voters, as a group, tend to gravitate toward female candidates. That’s especially true in general elections, but it also likely holds for a race like the Democratic primary.

Warren is not overwhelmingly popular among women right now, but she has had a small, consistent edge among women in recent polls. Our average of national polls taken between Aug. 1 and Sep. 1 do show Warren getting some extra support from women, though not to a huge degree. Women were 2.9 points more likely than men to support Warren on average, while both Biden’s and Harris’s backers were nearly identically split between men and women — with Biden getting the most backing from both groups. And according to Morning Consult’s weekly national primary poll, Biden’s support is particularly strong among black women, too.

Warren has a small advantage among women Average support among men and women for Democratic candidates who average 5 percent or more among all voters, according to national polls conducted Aug. 1 through Sept. 1 Candidate Women Men Gender Gap Elizabeth Warren 17.3% 14.4% +2.9 Kamala Harris 7.9 7.2 +0.7 Joe Biden 28.8 28.6 +0.2 Pete Buttigieg 4.9 5.7 -0.8 Bernie Sanders 15.5 17.9 -2.4 Source: Polls

There’s a certain resonance to the idea that women will rally around fellow women when they run for office — and recent polling has shown that Democratic women are particularly eager to elect a female president. But this doesn’t mean Warren — or any female candidate, for that matter — will overwhelmingly win women in the primary. For one thing, a gender gap in voting patterns may not tell us much about why women are supporting a particular candidate. Over the years, political scientists have found that even when women do vote for female candidates, it’s usually not because the candidate is a woman. Meanwhile, Warren’s emphasis on closing the wage gap or reducing maternal mortality might help her draw in more voters who care about gender discrimination, but those voters won’t just be women. After all, people’s reasons for voting are complicated, and women — even within a single party — are far from a monolithic voting bloc.

“What looks like women voting for women is usually just women voting for Democrats,” said Kathleen Dolan, a political science professor at the University of Wisconsin-Milwaukee. There’s very little evidence, Dolan said, to suggest that the desire to vote for a woman, even one who’s strong on women’s issues, binds female voters together — or if that desire exists, it’s weaker than the other forces that affect their political decisions.

Yes, women are disproportionately likely to vote for Democratic candidates, and female candidates are also disproportionately likely to be Democrats. But what Dolan and others have found is that what often looks like gender solidarity is in large part good old-fashioned partisanship. Take a look at the results of the 2016 election, when a majority of white women voted for Trump over Hillary Clinton, or the 2008 election, when Sarah Palin’s presence on the ticket did little to entice Democratic women, and it’s clear that party loyalty trumps female solidarity.

The more difficult question, of course, is what happens in a primary, where all the competition is between candidates of the same party. One recent study of judicial elections found that when party preferences were removed, women were substantially more likely to gravitate toward female candidates. That could indicate that women might be more likely to support female candidates in a primary, where party also isn’t a factor. But Alex Badas, a political science professor at the University of Houston and a co-author of that study, cautioned that voters don’t usually have much information about judicial candidates when they walk into the polling booth. “People know so much more about the presidential candidates,” he said. “So even if they can’t make a decision based on party, there are many other factors that could outweigh the candidate’s gender.”

In fact, other studies have shown that other parts of women’s identities — race, education, religion — seem to be more central to how they vote. Several studies of the 2008 primaries concluded that while many black voters did seem drawn to Obama because of their shared racial identity, Clinton didn’t benefit as much from women’s enthusiasm. And in the 2016 primaries, a strong sense of shared gender identity also wasn’t a predictor of support for Clinton.

This is not to say that gender doesn’t shape the way voters think about politics or choose which candidate to support. It’s possible that at least some Democratic women want to support Warren or Harris, but are holding back because they’re afraid that sexism will hurt a woman’s chances against Trump. For instance, Biden led the pack as usual in an Avalanche Strategy poll conducted earlier this summer, but when respondents were told they could wave a “magic wand” and make any of the candidates president, Warren was their top choice. And when respondents were asked what their “magic wand” candidate could change in order to win, the candidate’s gender was by far the most common answer, with women particularly likely to point to gender as a factor.

But whether a voter is a man or a woman likely matters less than how they think about gender when it comes to supporting a female candidate. One recent study found, for instance, that respondents’ gender was less predictive than their views about the prevalence of gender discrimination in determining their willingness to support a female candidate who had been attacked by her opponent. “Supporting gender equality, or being concerned about an issue like sexual harassment — that is a predictor of voting for women,” said Danny Hayes, a political science professor at George Washington University and one of the co-authors of that study. “But in a Democratic primary, that’s going to describe a lot of men as well as women.”

So Warren might still win over voters by emphasizing her policies on gender issues — her appeal just won’t be limited to women. In fact, there’s a good chance that the voters who are more likely to prioritize something like gender equality are also more likely to have higher levels of education, according to Hayes. That could partly explain Warren’s rise, since she’s performing especially well among white, educated voters.

But it also suggests that both Warren’s gender and her ambitious menu of policies to help women may not do much to help her broaden her coalition where she needs it most — particularly among black and Hispanic Democrats, who are largely sticking with Biden so far. “Warren might be able to chip away at Biden’s lead — but I wouldn’t expect it to be primarily driven by female voters,” Hayes said.

Meredith Conroy and Derek Shan contributed research