Shortly after, Sanders himself claimed that Clinton was not qualified to be president. He initially stood by the “unqualified” attack in a news release but later walked back the comments. Clinton laughed off the “ambitious” jab and called Sanders’s comments “silly” before saying she would “take Bernie Sanders over Donald Trump or Ted Cruz anytime.”

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Scuffles like these are highly unlikely to change the overall trajectory of the race, but they are troubling for this key reason: Attacks on female candidates as being “ambitious” or “unqualified” are exactly the reason that so many qualified women don’t run for political office in the first place.

Historically, being a woman was assumed to be a disqualifier in presidential politics. Until 1945, Gallup asked whether respondents would vote for a woman “if she were qualified in every other respect.” Since Victoria Woodhull’s 1872 race, female presidential candidates have often been portrayed as “unnatural,” intrinsically unsuited to public sphere, unviable, purely symbolic and incompetent.

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This discounting of women’s qualifications has several consequences. For one, it discourages women from running for office. They feel less qualified to run than do men with the exact same credentials. This gap in political ambition between men and women is partially responsible for the small fraction of women in elected office.

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Women who do run are held to higher standards on the campaign trail. This leads to pressure to project hyper-competence and preparedness. But this can produce a backlash: Women who assert confidence run the risk of provoking negative attitudes toward ambitious women. Extensive research illustrates that double standards about qualifications extend well beyond the political sphere.

Ironically, then, women who run win at rates equal to men and may actually outperform men once elected to office — but only because they are stronger candidates. But even after taking office, women are less likely to advance to a higher level of office partly because of their lower levels of ambition.

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Remediating the ambition gap would need to start in childhood. Women, compared with men, report that they engage less in political discussions as children. The political scientists Jen Lawless and Richard Fox argue that this communicates to women that politics is a “man’s game.”

But girls’ political ambition increases when they are exposed to high-profile role models. Our research demonstrates that even limited exposure to female candidates — such as having students interview a female elected official or having a female state senator as a guest speaker — can make young women more interested in political office.

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This research suggests that Clinton’s candidacy could have a similar, and perhaps larger, positive effect on how girls and women perceive their political voices and ambitions (something her campaign has consistently highlighted).

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Again, calling Clinton unqualified, or criticizing her ambition, probably won’t matter with regard to the outcome of the Democratic nominating contest. In fact, these attacks could even help Clinton by further mobilizing her supporters, who often feel that gendered concerns have been brushed aside by the mainstream media and that Clinton has been the focus of unusually high levels of scrutiny.

But these attacks on Clinton may matter more for the community organizer or school board member wondering whether she should consider an open House seat, or a college sophomore wondering whether she might run for student body president. If a woman who was a U.S. senator and secretary of state is “unqualified” and “too ambitious,” what does this say to women and girls considering a career in politics?