Libertarians hope they could be that plan C, picking up enough disgruntled Republicans and Democrats to prise open the duopoly that dominates American politics. This is not just the wishful thinking of party activists. As well as an ideology that they insist has broad enough appeal to pick up both Bernie Sanders supporters left with no one to vote for and disgruntled, socially liberal Republicans, the party has a technical claim to being taken seriously in the year of “Never Trump” and “Never Clinton”.  There are only three candidates for President on the ballot in all 50 states: the Republican, the Democrat and the Libertarian. If media interest is anything to go by, the Libertarian Party matters as it never has before. Fewer than 20 journalists applied for credentials for the Libertarian Party convention in 2012. This year the number is 250. How will a party whose 45-year history has been defined by a steadfast adherence to an inflexible set of core beliefs survive when it steps out of irrelevance and into the limelight?

Late on Sunday afternoon, James Weeks II, a large man with a thick sandy beard, walks onto the convention stage and into that limelight. He is a candidate for the party’s chairmanship. “Let’s have some fun,” he tells the assembled delegates, journalists and television cameras. He plays a song from his phone, placing the microphone on the lectern next to its speakers to fill the room with tinny country rock. He takes his jacket off, raises his hands above his head and claps along to the beat, urging the crowd to do the same. He removes the lanyard holding his convention credentials. He loosens his tie. And then it dawns on everyone: James Weeks II is going to strip.

With every piece of clothing he peels from his chubby body, every lasso-like swing of his tie above his head and every gyration of his waist, not only does it become clear that his candidacy for the chairmanship may not be entirely serious, it also becomes apparent that the Libertarian Party may not be as prepared, or even willing, to disrupt the duopoly as they say they are.

The crowd is split on the advisability of Weeks’s routine, which he says was the result of a dare made by “an important donor to my Sheriff campaign”. Some are disgusted, or at least think it unhelpful. “I do not want the world to think that is what libertarians are,” one exasperated delegate tells me. “I found that so offensive,” says another, “that it was a violation of the non-aggression pact,” citing what for many is the golden rule of libertarianism. (According to the late economist Murray Rothbard, a leading figure of the movement, the rule dictates that “no violence may be employed against a nonaggressor”; he described it as the “fundamental rule from which can be deduced the entire corpus of libertarian theory”. “NAP” badges are a popular accessory in Orlando.) Others whoop at what they see to be an exhilarating exhibition of the freedom they have come to Florida to celebrate and advance. A few even run on stage to fold a dollar bill under a thong that is perilously close to losing its grip on Weeks’s buttocks. I asked Weeks whether he thought his performance was helpful for the party. “It can’t be worse than Gary Johnson,” he replied as he climbed back into his trousers.