ORLANDO, Fla. — Delegates puffed on e-cigarettes between chants of “freedom!” Educational booths proclaimed the virtues of hemp, “trickle-up economics” and the literature of Ayn Rand. A woman on stilts wearing purple angel wings greeted activists as they milled between seminars on drug war policies and on “how to abolish the government in three steps.”
In a year when the two major parties are consumed by tensions, defections and chaos, the Libertarian Party, which sees itself as their alternative, displayed some of the same traits as it wrestled with nominating two former Republican governors for its presidential ticket at its annual convention over the weekend. But there was also a palpable sense of excitement at the event, held at a hotel here less than 10 miles from Disney World.
For an antiwar party that promotes legalizing marijuana and tearing up the tax code, 2016 has brought hope that acceptance in the political mainstream is imminent amid broad discontent with the probable nominees from the major parties.
“We have been given the gift of Trump and Clinton,” said Larry Sharpe, a businessman and candidate for the Libertarian vice-presidential nomination. “Their ears are open, and I want them to hear who we are and vote for us for who we are.”
The Libertarian Party is the country’s third largest by voter registration, excluding people who consider themselves independent, but it is often overlooked as a political sideshow with a hodgepodge of positions that many consider to be either overly liberal on social issues or too conservative fiscally.
With Donald J. Trump’s rise spawning a contingent of conservative Republicans who will not support him and backers of Senator Bernie Sanders feeling that the Democratic Party is favoring his opponent, Hillary Clinton, Libertarians think they are poised to peel away voters from both sides. The party aims to be on the general election ballot in all 50 states.
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“There are Republican voters who are going to feel cheated by the fact that their presidential nomination has been taken by a reality show star, and there are Democratic voters who are going to feel cheated when that corporate shill boxes out Senator Sanders at the convention in that rigged process,” Nicholas Sarwark, the Libertarian Party’s national chairman, said on Sunday. “When those people feel cheated, we present an option for them.”
Although only the most fanatical party loyalists feel confident about their chances of winning the presidency, many think that Libertarians are poised to win a record number of votes. Some believe they could steal a state, which no third party has done since George Wallace in 1968, or get enough votes to influence the election, as Ross Perot and Ralph Nader did.
More than disrupting the election, though, they see it as a golden opportunity for true national exposure and expansion. The party received more than a million votes in 2012, its most ever, and recent polling suggests a growing appetite for third-party candidates.
An NBC News/Wall Street Journal poll this month found that 47 percent of registered voters would consider a third-party candidate if Mr. Trump and Mrs. Clinton were the major party nominees. Political analysts were taken by surprise this spring when two separate polls showed Gary Johnson, the former New Mexico governor and the 2012 Libertarian Party nominee, pulling 10 percent and 11 percent of the national vote.
The party chose Mr. Johnson again as its standard-bearer at its nominating convention on Sunday. If he can get to 15 percent in polls, he can stand on the debate stage as the first third-party candidate to do so since Mr. Perot in 1992. The feat would provide a bounty of free news media attention for a party that does not have the money for expensive advertising or voter-outreach efforts.
Mr. Johnson believes that with sufficient exposure and a positive message he can attract both the young, progressive voters who are backing Mr. Sanders and Republicans who want limited government but fear that Mr. Trump would ratchet up spending and start trade wars.
“We should be portraying an optimistic message,” Mr. Johnson, dressed in a dark suit with no tie and wearing sneakers, said in an interview. “Life is good in America.”
Looking to add credibility to his campaign, Mr. Johnson is teaming up with William Weld, the former Massachusetts governor, as his running mate. Mr. Weld, who has compared Mr. Trump’s immigration policies to those of Nazi Germany, said he was reaching out to Republican donors who have decided that they cannot support their party’s presumptive nominee.
“I’m going to go knocking on every door I can to try to help us along,” Mr. Weld said.
As with Republicans and Democrats, the Libertarians displayed their own intraparty divides on Sunday during a raucous round of voting. Many delegates expressed concern that the party was becoming a landing ground for failed former Republicans and sacrificing its purity to appear more palatable. Mr. Johnson secured the nomination on the second ballot of voting, and Mr. Weld was forced to publicly promise his allegiance to the party before he was voted onto the ticket, also on a second ballot.
The possible effect of the Libertarians on the November election remains unclear, as most state polls have not included any of the candidates and the party is not yet on the ballot in every state.
Kyle Kondik of the Center for Politics at the University of Virginia said a ticket with Mr. Johnson and Mr. Weld could capture many votes in their home states of New Mexico and Massachusetts. Alaska, Arizona, Colorado and Nevada have also shown a propensity to find unconventional candidates appealing, he said, so the Libertarians could tilt close races there.
“The Libertarian ticket is kind of a mix of left and right,” Mr. Kondik said. “There is potential appeal for it to be a soft landing spot for voters of all stripes.”
Still, the climb will be steep. There were just 411,000 registered Libertarian voters as of February, and, Mr. Kondik noted, third-party candidates tend to underperform their poll numbers.
“Ultimately it would be a giant shock if they carried even one state,” Mr. Kondik said. “Perot never did, and he got 19 percent.”
Despite efforts to broaden their base and become an acceptable alternative to the American public, Libertarians battle perceptions that they are “Republican lite” or “old white guys.” The convention’s carnival-like atmosphere belied those caricatures: A cross-dresser clad in a leopard-print leotard strode across the stage with an umbrella to introduce one candidate, and professional dancers basked in strobe lights at a party before the candidates debated on Saturday night.
The debate itself offered a window into some of the challenges the Libertarians face as they try to package themselves for broader consumption while sticking to their limited-government principles. The conversation often drifted into strained arguments about how common sense would keep heroin out of the hands of children, how government-issued driver’s licenses are unnecessary — one suggestion was a pink flashing light for new drivers — and how public infrastructure could be built without taxes.
“Who will build the roads?” Austin Petersen, a presidential candidate and founder of The Libertarian Republic, a magazine, said during the debate. “Where we’re going we don’t need roads.”
There were also lesser-known presidential hopefuls such as Vermin Supreme, a performance artist who wandered the event with a rubber boot on his head, and Marc Allan Feldman, who began his speech with a Libertarian rap in which he proclaimed, “Republicans and Democrats are wack.”
And then there was John McAfee, the antivirus software pioneer who in 2012 was in hiding in Belize after the police there sought him for questioning in the death of his neighbor. Mr. McAfee, who presented a campaign video declaring, “Here’s to the crazy ones,” doused some of the enthusiasm when he said none of the candidates — himself included — had any chance of becoming president.
Win or lose, most remained encouraged that this year will be important for the Libertarian Party and that even if they do not take the White House this time there are opportunities to win state and local races and to convert Republicans and Democrats.
Scott Scrimshaw, a community chaplain from Oregon, switched from Republican to Libertarian six months ago after he surveyed the field of candidates and found himself disappointed. A longtime admirer of Ronald Reagan, he said that he could not trust Mr. Trump with his vote and that he did not want to choose between “the lesser of two evils.”
“I feel we are really on the edge of entering a new era of American politics,” Mr. Scrimshaw said. “The era of the third party.”