NEW YORK—The official position of the Libertarian Party, currently America’s third-most-popular presidential ticket, is that nobody won last week’s presidential debate, and America lost. But that is not the position of the party’s vice presidential candidate, Bill Weld.

“I thought Mrs. Clinton was very good,” Weld, the former governor of Massachusetts, told me the morning after the debate, settling his tall frame into a cheap, vinyl-seated chair. “She kept her game face on, and Mr. Trump did not. She was in control of herself.” Trump, he noted, had not been able to stop himself from taking the bait every time he was confronted with a sensitive topic.

Weld poured salt and then pepper into his left palm before sprinkling them onto his steam-tray Western omelet from the breakfast buffet of his Manhattan Holiday Inn. He was, he confessed, a bit embarrassed to be staying there. But it was in convenient proximity to CNN and CBS—since the Libertarians can’t afford ads, their campaign strategy revolves around seeking media attention—and usually priced at $110 a night. The Libertarian ticket is, appropriately, nothing if not frugal.

The question that always haunts third-party tickets is whether they will play spoiler to one of the major parties. This year, the Libertarians were initially assumed to be a problem for the Republicans: The ticket consists, after all, of two former Republican governors, Weld and former New Mexico Governor Gary Johnson. For the many GOP voters repulsed by Trump, the Libertarians could be an appealing alternative. But Johnson and Weld also appear to be drawing votes from Clinton, particularly from young people who prefer their live-and-let-live idealism to her baggage-laden wonkery.

This is not the way Weld thinks it ought to be. He believes Clinton is wrong on policy, particularly fiscal and military matters—but Trump is unthinkable. To some, that discrepancy means he ought to drop out and throw his support to Clinton. “We have a lot of New York City liberal Democrat friends, and they are very anxious,” he told me wryly. In the last few weeks, he’s received dozens of emails and phone calls from strangers to that effect—he is not sure how they got his contact information.

Weld’s answer to these critics is, essentially, that he is more good to their cause where he is. “I have a platform,” he told me. “As long as I’m a candidate for a legitimate political party, people pay attention to what I say, and I have a lot to say about Mr. Trump.” In the next few weeks, he plans to make his position clear, he added. “We are drawing 50-50 [from the two major parties], but that’s before people hear everything I have to say about Mr. Trump for the next seven weeks.”

The distaste many Americans feel for the two major candidates this year would seem to create a historic opening for a third party. According to one analysis, more than a quarter of American voters dislike both Clinton and Trump. And the Libertarians have never had a ticket as well credentialed as Johnson and Weld, both two-term governors well regarded in their home states. Yet the Libertarian ticket has failed to catch fire, failing to meet the 15 percent polling threshold that would get Johnson and Weld into the debates, which would expose them to a wider audience and potentially catapult them into real contention.

Johnson’s deficiencies as a candidate may be part of the reason. On MSNBC last month, he responded to a question about the humanitarian disaster unfolding in Syria by asking quizzically, “What is Aleppo?” And just this past week, asked to name a foreign leader he admired, he drew a blank. It fell to Weld, who was once nominated by Bill Clinton to serve as U.S. ambassador to Mexico, to fill in the name he was grasping for. (Weld never got to serve in Mexico City: His nomination was torpedoed in 1997 by congressional conservatives who saw him as a squishy Northeastern moderate.) As one observer remarked on Twitter, “In a year when a sane Libertarian might actually have a chance, they chose Mr. Bean.”

(On my way to meet Weld for breakfast, I ran into Johnson and asked him about his running mate. Johnson responded with his typical off-kilter brio. “He’s the other half of the ticket!” he exclaimed brightly, as if that fact somehow constituted praise. More seriously, Johnson said Weld, whose second term overlapped with Johnson’s first in the 1990s, had been a sort of role model to him in the way he defied convention and party orthodoxy.)

Johnson’s flaws have led some to wish the ticket were reversed. “I wish Bill Weld were at the top, because I knew Bill Weld as the governor of my state of Massachusetts, and he was a terrific governor,” Mitt Romney said in June. “I think he’d be a great president.”

When I asked Weld about this sentiment, he replied, “I hear that a lot from people in Massachusetts and New York who’ve known me for 20 years and don’t know Gary from a cord of wood.” But, he added, when the candidates travel west of the Mississippi, it’s Johnson who’s mobbed by fans.

Amiable and unabashedly patrician, Weld, who is 71, has side-parted white-blond hair, a drooping, grooved face, and an appealingly sardonic affect. His pinstriped black suit is a little baggy; his tie is decorated with blue and pink seashells. The descendant of an aristocratic New England family, Weld has always carried his heritage lightly: Teased for his forebears’ having come over on the Mayflower, Weld once replied, “Actually, they weren't on the Mayflower. They sent the servants over first to get the cottage ready.”

As governor, Weld got along well with the Democratic legislature, balanced the budget, and cracked down on crime. In 1996, he memorably dove into the Charles River, along with a Democratic state senator, to celebrate the passage of bipartisan river-protection legislation. Weld’s Democratic opponent in his first race was John Silber, a philosophy professor whose populism now reads as Trumpian—he was known for his erratic manner and offensive statements. As a slogan against him, Weld’s campaign adopted a line that resonates this year: “He’s not just mad at them, he’s mad at us.”

Since leaving office, Weld has been a political journeyman. He ran unsuccessfully for the U.S. Senate against John Kerry in 1996, briefly relocated to New York and ran for governor there, and raised money for the presidential campaigns of Pete Wilson in 1996 and Romney in 2008 and 2012. He likes being in the arena, he told me, and took little convincing when Johnson first floated the idea of joining him on the ticket several months ago. The two men scheduled a phone call. “I could hear [Johnson] rearing back on his hind legs to deliver a lengthy sales pitch,” Weld recalled. “I said, ‘Gary, save your breath. I think this is a good idea.’”

Weld has always been fiscally conservative and socially liberal, he says: “I’ve self-identified as a small-l libertarian since I was in law school.” On military matters, he was once a typical GOP hawk, but events in Iraq, Libya, and Syria have made him reconsider and he now supports Johnson’s more “restrained” posture. He has found it liberating to belong, for the first time, to a party whose agenda he largely supports. “I never agreed with the Republicans’ conservative social policies,” he said. “So now I’m, like, ‘free, free at last!’ Because I agree with the social policies of the Libertarian Party as well as the fiscal policies.”

To get on the ticket, Weld was required to attend the Libertarians’ convention in Orlando in May, an experience he described to me as “bracing.” Many movement Libertarians regard Weld and even Johnson as unacceptably heterodox. “They booed Gary for supporting drivers’ licenses and saying he would have signed the Civil Rights Act of 1964!” Weld marveled. And then there was the candidate for party chairman who stripped down to his briefs onstage. “He did not have the figure for that,” Weld deadpanned.

Weld’s nomination was approved on the second ballot with just 50.5 percent of the vote—a close call but, on the whole, not too difficult a process. “I feel like Rosie Ruiz, the woman who snuck in at the end of the Boston Marathon” in 1980, Weld said. Ruiz took the subway to within a few blocks of the finish line, ran the rest of the way, and was briefly declared the women’s winner of the race. “Then they figured out there was a problem, because she wasn’t at any of the checkpoints, and they got footage of her coming out of the subway,” he continued. “I get to do a national campaign in five months!”

This is the point of running for Weld: He relishes “the joy of the fight” and has always wanted to be involved in politics at the national level. But he also is disturbed by the direction of the national discourse.

“The way Washington is trending, the wacko left and wacko right are heaving more closely into view,” he said. His erstwhile party particularly troubles him. “I think the Republican Party’s going to split, this cycle or the next cycle,” he said. “One party will be Donald Trump’s party, which you could call the Know-Nothing Party,” and which, like the Know Nothings of the 1850s, would be “based on hatred of immigrants and conspiracy theories and violent rallies.” The other part, the “nice half of the party,” would, he hopes, find new allies and persevere.

For now, Weld plans to continue to stand for his ideas, a task that has unintentionally taken on more urgency in this extraordinary political year. “The campaign started out as pure joy,” he said, sipping his coffee and gazing into the distance. “And then an element of patriotic duty crept into it.”