Former Secretary of State Hillary Clinton and Sen. Bernie Sanders (I-Vt.) talk over each other during a Democratic presidential primary debate. (AP/Mic Smith)

Dishonest, shrill, and frumpy: Not just Hillary Clinton’s Republican opponents but also media commentators have hurled these criticisms, during this election cycle. And most Monkey Cage readers will recall the fuss about Clinton’s debate bathroom break.

Given such gendered background noise, it is certainly tempting to blame Clinton’s primary losses on sexism — or contrarily, to say that Clinton’s victories mean she has overcome sexism.

But do these gendered narratives affect whether voters cast a ballot for Clinton?

That’s not so clear. Research suggests that the way voters view female candidates is actually much more complicated.

Is voter sexism a problem for female candidates?

Voters view the presidency as a masculine position. Research shows that voters expect the president to display masculine qualities, and, well, to be a man. Consequently, voters might see female candidates as lacking the “right stuff” for the presidency. Past research, for example, finds that some voters do prefer a man in the White House — but only when they don’t know the candidates’ parties.

Studies (like this one and this one) that mention a candidate’s party find that once people know the candidates’ parties, voters care more about electing their own party’s candidate than whether that candidate is male or female.  (Of course, it’s different when both candidates are in your party; we’ll look at primary voting below.)

Still, voter sexism could hurt female candidates if they’re hampered by voters’ beliefs that women are, or should be, like feminine stereotypes: caring, emotional, and weak. These qualities don’t quite match up with how we think about political leaders.

To find out whether that’s true, I conducted a series of experiments specifically designed to measure whether people think female candidates have these feminine qualities. In both studies, participants were told a male or a female candidate of their own party was running for Congress. I then measured whether their votes might be influenced by perceptions of those feminine stereotypes, asking individuals to rate how strongly they thought each candidate was warm, soft, distant, harsh, and so on.

Even using implicit and subconscious measures of stereotyping, I found voters did not automatically attribute feminine qualities to the female candidate. Voters thought the female candidate was just as caring as the male candidate — and voters did not think either candidate was all that caring. But this didn’t mean voters thought the female candidate was any more cold and distant than the male candidate.

Basically, voters thought about the candidates in gender-neutral ways.

When choosing between a female and a male candidate of the same political party, voters were just as likely to vote for the female as they were for the male candidate. In fact, one study found a slight edge for female candidates.

Feminine stereotypes have no statistically significant effect on support for the female or the male candidate. Under these low information conditions of shared partisanship, feminine stereotypes just don’t seem to matter.

A number of other recent studies also find that voters don’t automatically think all female candidates are soft and passive. In fact, voters only perceive feminine stereotypes in female candidates when female candidates describe themselves as warm, caring, and so on.

Of course, that’s if the voter and the candidate are in the same party. So do female candidates have a harder time winning over voters from the other party?

In another experiment, participants read about a female or male candidate of the other political party; she was described as having feminine qualities. The opposing partisans said they wouldn’t vote for her, using precisely those feminine stereotypes to explain why. That downgrading of the feminine woman came out whether it was Democratic voters evaluating Republican women or Republican voters evaluating Democratic women.

But if we described the male candidate using such feminine-inflected words — warm, caring, and the like — the opposing partisans didn’t hold it against him. And when we described the female candidate in gender-neutral ways, the opposing partisans said they were just as likely to vote for her as they were for a male candidate in that party.

In other words, if Clinton becomes her party’s nominee, her toughest audience won’t necessarily be fellow Democrats, but Republican voters.

In sum, little research suggests that voters are overwhelmingly sexist against female candidates. Sure, some voters may harbor sexism and some voters may view women running for office as soft and passive. But unless they’re triggered by specifically sex-inflected descriptions of the opposing party’s female candidate, most voters focus on party rather than gender.

Couldn’t sexism and stereotypes still be a problem in the Democratic primaries?

Over the last six months, Clinton has spoken extensively about women’s issues. She’s touched on being a feminist, on the need for pay equity, and on the need for better family leave policies in the U.S. This has led some media critics to suggest that Clinton is pandering to voters by playing “the gender card.

But here again, the strategy is actually more complex. Yes, Clinton’s campaign may be trying to position her gender as a plus in the Democratic primaries. And yes, some voters might even support Hillary just because she is a woman.

It’s true that female Democratic voters tend to support female candidates. But what we call gender affinity isn’t just based on shared gender; it’s based on shared convictions of what’s important. Essentially, Democratic women see other female candidates, Democratic and even Republican, as being more likely to support issues that will improve the lives of women. And they’re right. Research shows female lawmakers actually are more likely to support legislation that improves the lives of women.

Voters care more about partisanship then they do about a candidate’s gender. But does gender affect them when choosing between a man and a woman of the same political party in a close race? Here, gender might play a more subtle role. Research suggests that Democratic female candidates win their primaries at the same rates as their male counterparts.

But female candidates are more likely to face tough primary challenges from high-quality opponents. This suggests female candidates may face more electoral hurdles in primary elections compared to male candidates — who, at least at the congressional level, often face uncontested primary elections.

But female candidates can overcome these tough primary challenges. They just have to be much more qualified then male candidates. In the Democratic primary, Clinton may need to demonstrate her ability, qualifications, and experience much more than her opponent.

Campaign commentators will continue to talk about Clinton’s gender, debating whether she is too feminine, too masculine, or wearing the right pantsuits. But for most voters in the Democratic primary, outright voter sexism is not an obstacle for Clinton. It’s more complicated than that.

Certainly, some voters in the Democratic primaries are levying gendered attacks against Clinton. But many of these voters were not going to support Clinton anyway. The voters who may be most likely to fall back on feminine stereotypes are the undecided primary voters. These undecided Democratic voters could see Clinton’s gender as a benefit inferring that she will support progressive women’s issues. Alternatively, they could see Clinton’s gender as a bane inferring that she is unqualified for the presidency. And for many of these voters, Clinton’s gender might not matter at all.

Nichole Bauer is an assistant professor of political science at the University of Alabama.