“I would be very troubled if someone were about to go to jail for something like this that happened 40 years ago,” said Nancy Gertner, a retired federal judge who has written extensively in defense of women’s rights in sexual harassment and sexual assault. Still, she said, “With respect to the Supreme Court you’re dealing with an elite position which is a privilege to be confirmed for. And arguably the standards are much higher.”

Judge Gertner noted that she had raised two teenagers — “teenage boys are nuts,” she said — and she has seen how allegations, even when found to be false, can unfairly tarnish young men. Last year, she and three other Harvard Law School professors urged the Department of Education to reassess Obama-era guidance to colleges on dealing with allegations of sexual assault, arguing they had encouraged colleges to adopt definitions of misconduct that are “seriously overbroad.”

“Should she be believed? I don’t know,” she said. “What does one do about an accusation that is this old? I’m not sure. But you’re talking about a different kind of position.”

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Much hangs in the balance. Judge Kavanaugh would fill what has been a swing seat on the court, and would likely be a decisive vote for a strengthened conservative majority. The midterm elections on Nov. 6 could flip control of the Senate, giving Democrats the power to veto any of Mr. Trump’s nominees for the next two years.

The allegations also come in a defining political moment for women, who are energized as voters and running for Congress in record numbers — in both cases, mostly as Democrats. It’s far different than 1991, when Ms. Hill reluctantly made allegations of sexual harassment against Judge Thomas during his Supreme Court confirmation hearings. The male senators who cast doubt on her were a bipartisan group — almost unthinkable in today’s polarized setting. And a cultural reckoning on sexual assault in recent years — in the Catholic Church, in elite boarding schools, and in the highest ranks of Hollywood — has established that crimes committed several decades ago are crimes all the same.