And, in what is one of the most difficult barriers for Mrs. Clinton to break through, young people often display little understanding of how a protest vote for a third-party candidate, or not voting at all, can alter the outcome of a close election.

The vast majority of millennials were not old enough to vote in 2000, when Ralph Nader ran as the Green Party nominee and, with the strong backing of young voters, helped cost Vice President Al Gore the presidency.

“Ralph who?” said David Frasier, a junior at Charleston Southern University.

“Didn’t he kind of come in at the last minute and kind of alter the votes or something?” Mr. Frasier, 26, asked, his memory barely jogged. “I was too young to remember.”

The Clinton campaign’s biggest problem with young voters could be summed up by Mr. Frasier. He is liberal-minded and voted for Mr. Sanders in the South Carolina primary. But he is not likely to vote for either Mrs. Clinton or Donald J. Trump, the Republican nominee, both of whom he called “pawns and puppets.”

Echoing sentiments that seem to be driving many young people away from politics, Mr. Frasier said he felt powerless to bring about change through voting. “I don’t feel like we have control,” he said. “I kind of feel like this whole election is just playing the American people.”

Mrs. Clinton’s weakness with young voters is largely because of the support third-party candidates are drawing away. Mr. Trump’s support among the young has hovered around 25 percent in recent polls.

More than a third of voters 18 to 29 said in the latest New York Times/CBS News poll that they would vote for either Gary Johnson, the Libertarian candidate, or Jill Stein, the Green Party candidate: Mr. Johnson had the support of 26 percent of those voters, and Ms. Stein had 10 percent.

Given the choice of just Mrs. Clinton and Mr. Trump, 10 percent said they would not vote at all — double that of any other age group. An ABC News/Washington Post poll this month found a similar level of support for third-party candidates: 20 percent for Mr. Johnson and 6 percent for Ms. Stein among registered voters ages 18 to 39.

Photo

Ralph Nader at the University of Michigan-Dearborn in October 2000. Votes for him contributed to the loss of the Democratic candidate, Al Gore. Credit Monica Almeida/The New York Times

The stubborn popularity of the third-party candidates has become a concern to Mrs. Clinton and her allies. So far, the support for them has not softened, as it often does in the fall.

“Historically, that’s what has happened,” said Jefrey Pollock, who is advising the “super PAC” working on Mrs. Clinton’s behalf, Priorities USA. “But history isn’t repeating itself right now, which is one common theme of this election cycle.”

Some of Mrs. Clinton’s advisers believe that the absence of Mr. Johnson and Ms. Stein from the debate stage on Monday — both failed to meet the 15 percent polling threshold to qualify — will help bring down their numbers. In the meantime, the Clinton campaign has accelerated its aggressive courting of young voters.

That effort involves enlisting Mr. Sanders and Senator Elizabeth Warren of Massachusetts, two figures popular with young people, to make the case that Mrs. Clinton cannot make for herself.

“I suspect that I know about as much about third-party politics as anybody in Congress,” Mr. Sanders, an independent himself until he decided to run for president as a Democrat last year, said in an interview. “And I want anybody who’s thinking about voting against Hillary Clinton, and casting a protest vote because she is not all they would like her to be, to understand what the consequences for the country and the world will be.”

As interviews with young voters show, it is a hard sell.

Nick Chanko, 20, is a student at McGill University in Montreal who plans to vote in his home state, New York. A registered Democrat, he said he would either vote for Ms. Stein or not vote at all.

“I feel like a lot of the stuff Hillary does, you can see when she is trying to, like, earn the youth vote, and it just doesn’t work,” Mr. Chanko said. “It’s just kind of cringeworthy. She just doesn’t seem genuine.”

Mr. Chanko said he did remember Mr. Nader’s candidacy but thought it was unfair to blame protest votes for spoiling an election.

The debate over the merits of casting a third-party ballot can seem endlessly circular.

“I understand the frustration, but channel that frustration into making government work, not into throwing away your vote,” Ms. Warren said in an interview. “They should not trust the system,” she added. “But the answer is to seize the system and make it work for the people, not to just turn it over to the bigots and billionaires.”

The possibility of young voters’ staying away from voting booths in droves come November is very real. Turnout rates among Americans ages 18 to 24 dropped significantly in 2012, to 41 percent from 49 percent in 2008.

This is both a frustration and a paradox to people who try to get them to the polls.

This huge pool of potential voters has been the animating force behind the largest new social movements on the left, from Occupy Wall Street to Black Lives Matter. Yet many do not equate voting with social change.

“They’ve shown they have the civic muscle to get things done,” said Allegra Chapman, the director of voting and elections at Common Cause, a nonpartisan civic engagement group. “The question becomes, how do we translate this civic muscle into the kind that shows up and has a presence at the ballot box?”

Repairing the mistrust millennials have of institutions and the political system is not easy.

Nathan Mowery, a 26-year-old federal contractor who lives in Gainesville, Va., said that as a Muslim, he would find it hard to vote for Mr. Trump. But he said that he found Mrs. Clinton uninspiring and that he planned to vote instead for a third-party candidate. He was unapologetic about his choice.

“I’m casting a protest vote because it makes it visible to major parties that there are people who are motivated to vote but are unwilling to vote for either of them,” he said. “I hope that whoever runs in 2020 will get their act together and one of the parties will put somebody up that younger voters can align themselves with.”

Asked if he remembered Mr. Nader, Mr. Mowery captured the essence of the Clinton campaign’s fears about young voters.

He said he was vaguely familiar with Mr. Nader as another third-party candidate. “Other than that,” he said, “I don’t know much.”

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