Jennifer L. Lawless and Danny Hayes, authors of Women on the Run: Gender, Media, and Political Campaigns in a Polarized Era, help us understand the precise causal mechanism. There are lots of reasons women may be disinclined to run for office — including the broad suite of structural barriers related to gender norms and family life that tend to limit women's access to all manner of high-powered jobs — but one reason is the perception that a woman candidate is likely to be unfairly disadvantaged.
The election of a high-profile woman gives other women residing in the state confidence that a woman can win, making them more likely to run and making more women likely to win....
Electing a woman governor has a bigger impact than electing a woman attorney general. That is no surprise — the governor is a higher-profile, more important role. But even so, governors are relatively obscure. A 2007 Pew survey showed that just 66 percent of the public could correctly name their state's governor.
The president, by contrast, enjoys near-universal name recognition. Indeed, even back in 2007 Clinton was correctly identified by 93 percent of respondents. Consequently, you would expect an impact that's quite a bit larger than the gubernatorial one.
But the impact would also exert itself across a much larger scale, since the president covers the entire country and not just one state. It would also have knock-on effects, since if a Clinton presidency inspired one additional woman senator she, in turn, would inspire more down-ballot runs....
Even all this would be of pretty narrow concern except for the fact that it turns out that gender is a significant driver of legislators' behavior.
John Sides summarized some of the research last March:
For one, women are more likely than men to advocate for issues often associated with women’s interests — child care, women’s health, abortion, pay equity and the like. There are many studies, but see Michele Swers’s two books to start with. This shows up, for example, in in floor speeches and legislative debates, where women are more likely to discuss issues in terms of women’s interests. (Women are also more likely than men to give floor speeches, period.) [...]
Other research suggests that women may be more effective legislators than men. Craig Volden, Alan Wiseman and Dana Wittmer find that, within the minority party, women are able to get their sponsored bills further through the legislative process. Sarah Anzia and Christopher Berry have shown that women sponsor and co-sponsor more bills than men do, and deliver about 9 percent more funding to their districts.
What's even more striking is that these differences seem to grow with scale rather than shrink.
Tali Mendelberg, Christopher Karpowitz, and Nicholas Goedert show that "when women are many, they are more likely to voice women’s distinctive concerns about children, family, the poor and the needy." What's more, when women are more numerous and therefore more vocal on these topics, men become more vocal too, and "these effects are associated with more generosity to the poor."
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