Like any candidates, these women are facing attacks on their policy positions and credibility. For instance, in Rhode Island, the president of the teacher’s union said that Gina Raimondo, the first woman to serve as governor in the state, had “turned her back on classroom educators.” In Maine, which has never had a woman governor, an op-ed attacked Mary Mayhew, a Republican candidate, for not caring for those on welfare in the state.

According to our research, certain kinds of attacks may be especially potent against women candidates.

Much of the political science literature on negative campaigning suggests that it has no consistent overall effect on voters; it doesn’t change voters’ minds or suppress supporters’ turnout. But we found an exception: women candidates (and to a lesser extent men) are vulnerable to attacks that emphasize traits and policies stereotypically associated with their gender and party — like assertiveness or compassion, and defense or education policy.

Here’s how we did our research

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If a candidate is attacked on her “home turf” — meaning the traits or issues traditionally associated with that candidate’s party and/or gender — how does it affect voters? To find out, we ran two survey experiments in the fall of 2015 with a total of 1,700 participants using Amazon’s Mechanical Turk, an online platform where researchers can hire people to take surveys.

In the two experiments, participants were randomly assigned to read one of four fictional newspaper articles that attacked a hypothetical candidate in a primary race for a state senator nomination in an unspecified state. The attack challenged the candidate’s competence on a stereotypical feminine or masculine policy issue — education or security — or trait — criticizing their track record on collaboration or strong leadership. We varied the party and gender of the targeted candidates, which allowed us to compare how voters reacted to these kinds of attacks when they were aimed at men or women of both parties.

For example, the article that attacked the candidate about a stereotypical feminine trait charged that the candidate — called either Patricia or Tom Johnson — “just does not have interpersonal skills needed to work with other representatives toward our policy goals.” The article that attacked on a stereotypical masculine trait included such charges as that Johnson “just does not have the confidence to speak up and pursue ideas in policy.”

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Meanwhile, the attack on a stereotypical feminine issue charged that Johnson broke campaign promises about education reform, saying “The bottom line is, on an education platform but did not make any policy changes in this area.” The comparable masculine issue attack accused Johnson of working to “drain resources dedicated to public safety.”

We then asked respondents to rate the attacked candidate, Johnson, on a host of traits and policy strengths. They also indicated how likely they were to vote for Johnson on Election Day.

You can see the complete experimental articles and information about our sample here.

Attacks hurt female candidates more than male candidates

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When a woman was attacked for poor performance on a stereotypical feminine issue like education, voters saw her as less competent and were less likely to vote for her. This attack harmed male candidates as well, but the effect was notably weaker.

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The difference was especially strong when women were attacked on a stereotypical feminine trait. Women accused of being uncooperative or “not a team player” were seen as having fewer positive feminine traits overall and respondents were less likely to vote for them. While both men and women took a hit for the feminine trait-based attack, the effects were twice as large for female candidates.

That varied by the candidate’s party. Democratic women were seen as less electable than Republican women when attacked for failing to be compassionate or collaborative; that’s probably because both women and Democrats are expected to have these traits., a Democratic woman who faced a feminine trait attack was rated 60 percent lower than a Republican woman when evaluated for such positive feminine traits as compassion and sensitivity.

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On average, attacks on male candidates’ masculine traits hurt them less than female candidates were hurt when attacked on feminine traits. When it came to attacks on issues, however, that varied by party: male Democrats were hurt more when attacked on both “masculine” and “feminine” policy issues., when attacked on education, the reduction in respondents’ willingness to vote for the male Democrat was 60 percent larger than for the male Republican.

How would our results translate to the real world?

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In the real world, women candidates for executive offices — like governor — might be even more hurt by stereotypical thinking and attacks. And those are coming fast and furious. For example, Iowa Gov. Kim Reynolds has faced intense criticism on masculine policy issues such as the state budget, the prison system, and also “feminine” issues like child welfare. How will those affect her bid for reelection?

Of course, it’s hard to know exactly how our findings might translate to the real world. Our experiments focused on voter reactions to a single gender-stereotypical attack, with no context; respondents didn’t get to hear how the attacked candidate replied or observe him or her in action. Women candidates may well have effective strategies for combating stereotype-based attacks, neutralizing them through their own messaging. That would fit existing research that finds that American voters aren’t affected by gender stereotypes.

Current gubernatorial campaigns have gone negative early into primary season. Perhaps in upcoming races we will be able to observe for ourselves how much gender dynamics matter.

Erin C. Cassese is an associate professor of political science at West Virginia University.