McAfee is a commanding presence as he ambles through the convention hall. He is friendly and — once you get past the documentary film crew following his every move — approachable. Delegates and even journalists are taken under his arm and spoken to in a way that inspires confidence. Supporters ask him for a photograph and he hugs them like old friends.

Saturday night’s presidential debate begins once Libertarian-sympathising country singer Jordan Page has finished a warm-up set that includes a song called “Arm Yourselves.” Broadcast on C-Span, the debate demonstrates the ideological breadth of the party, the limits of Johnson’s appeal to his party’s delegates and, above all, the possible limits of his party’s appeal to America. As well as Johnson, Petersen and McAfee, Dr Mark Allen Feldman — “the anaesthetist who won’t put you to sleep” — and Daryl Perry, from “the libertarian wing of the Libertarian Party”, take part. The questions tackled by the candidates are nothing like those posed to their Republican and Democratic counterparts; most of them have nothing to do with the issues of day or the concerns of undecided voters. Was America right to enter the First World War? What about the Second? Would you abolish the Federal Reserve? Would you close down the Department of Education?

McAfee uses his opening statement to tell the delegates that none of the party’s candidates will make it to the Oval Office. “If I get one more question about what I will do on my first day in office,” he says, “I will lose it up here.”

Daryl Perry is asked what he thinks the legitimate function of government is. “Your question implies there is a legitimate function of government,” he replies. (In the previous evening’s vice-presidential debate, his notional running-mate William Coley is asked a question about which politically achievable reforms to the tax code he would advocate. “I’m not interested in politically achievable goals,” he answers. “We’re Libertarians. Taxation is theft. Cut it all! Keep cutting!”)

Proceedings reach previously uncharted depths of obscurity when the candidates are asked whether they believe the government has the right to issue driving licences. Johnson says he does; after all, he points out, what about blind people? He is the only candidate on stage that thinks any kind of state involvement in deciding who can and cannot drive is a good idea, a position that prompts boos and cries from the crowd: “Bullshit!”, “Go home, statist!” Throughout the debate, Johnson’s answers get nothing more than polite applause. Dr Feldman raps his closing statement — “I’m that no-pain, no-gain Libertarian/That get those petitions signed in the rain Libertarian” — and the crowd goes wild.

In the end, Johnson and Weld win the nominations they came for. After two rounds of voting, a majority of delegates accept that the two former governors are the only hope they have. The convention is less a choice between credible candidates, more a kind of Libertarian inquisition into the party’s only realistic option, a test of the sincerity of Johnson and Weld’s conversion to the cause. Before he is nominated, Weld is forced onstage to prove his loyalty to the cause. “It’s been 14 days since I became a Libertarian,” he tells the delegates, “and I feel better for it. I think I’ve become a better Libertarian every day . . . I pledge to you that I will stay with the Libertarian Party for life. Frankly, it’s a relief not to have to carry the Republican’s anti-choice, anti-marriage, anti-freedom agenda on my back.” The delegates buy it.