Women also tend to be viewed as unlikable based on their ambition. Harvard researchers found in 2010 that voters regarded “power-seeking” women with contempt and anger, but saw power-seeking men as stronger and more competent. There is often some implication of unscrupulousness in descriptions of female candidates as “ambitious” — an adjective that could apply to any person running for president but is rarely used to disparage men. Within 24 hours of Ms. Harris’s campaign kickoff, some critics were bringing up her onetime relationship with a powerful California politician, Willie Brown — a common tactic faced by women that sexualizes them and reduces their successes to a relationship with a man.

And if a narrative of unlikability takes hold, it can influence voters without their even realizing it.

“I actually heard so often that people didn’t like her and she was unlikable that I started to think, ‘I don’t know if I really like her so much,’” Heather Pasqualino Weirich, a Democrat from Phoenixville, Pa., said of Mrs. Clinton, whom she later supported. “I realized I had no reason why I didn’t like her.”

Masculinity and femininity

The qualities voters tend to expect from politicians — like strength, toughness and valor — are popularly associated with masculinity. This often means that from the moment a man steps onto the campaign trail, he benefits from a basic assumption that he is qualified to run, while a woman “has to work twice as hard to show that she’s qualified,” Ms. Hunter said.

“People just start off assuming that you care about the soft issues, you care about hearth and home, and that you can’t know anything about finance or military,” said former Senator Carol Moseley Braun, who ran for the Democratic presidential nomination in 2004.

For many years, female candidates tried to adopt the characteristics voters wanted to see — to act, stereotypically speaking, like men. This worked for some but also brought pitfalls. For one thing, it did not challenge the premise that masculinity is better suited for leadership. It also opened women up to a familiar double standard: A man who speaks authoritatively might be confident or opinionated, while a woman who does the same is arrogant or lecturing. Most pressingly, it created a backlash among some voters who saw women acting “like men” and deemed them inauthentic.