AS THE likely presidential nominee of the Libertarian Party, Gary Johnson has a lot to be modest about; and he is. “Everybody I meet seems to like me,” says the two-term former Republican governor of New Mexico. “But I’m a Libertarian, so doesn’t that denote there are some loose screws out there?” He leaves the question hanging.

Tiny, electorally trifling and obsessed with guns and weed, cherished emblems of its 11,000 members’ freedom, the party has never mattered in national politics. It is by some measures America’s third-biggest—yet not flattered by that comparison. In 2012 Mitt Romney crashed to defeat with 61m votes; Mr Johnson, who ran for the Libertarians after failing to be noticed in the Republican primaries, won 1.3m. Yet he could be about to improve on that.

Mr Johnson and his running-mate, Bill Weld, a former governor of Massachusetts, are expected to emerge from the Libertarians’ convention in Orlando on 30th May with the party’s ticket. If so, he could feasibly launch the biggest third-party run since Ralph Nader won almost 3% of the vote for the Green Party in 2000—including 100,000 votes in Florida that may have cost Al Gore the presidency. Or he could do better; a poll by Monmouth University put Mr Johnson on 11% in a three-way race with Donald Trump and Hillary Clinton. That was especially creditable given how little he is known; he figured in almost no national polls in 2012. It has encouraged Mr Johnson to think he could register the 15% vote-share that would guarantee him inclusion in this year’s televised debates.

With publicity, he could catch on. He has the accomplishments of a chest-beating conservative hero—he is a self-made millionaire, triathlete and razor-beaked deficit hawk; he vetoed 750 spending bills in New Mexico. He is also a sometime dope smoker (he resparked his youthful habit in 2005 to manage the pain from a paragliding accident), who comes across as almost goofily unaffected. He speaks in horror of the disdain many Americans show for Mexican immigrants—whom he calls “the cream of the crop”—as if it were borne of some crazy misunderstanding, rather than embedded nativist resentment and economic anxiety. Voters sick of political polish might like the mix: he really is authentic. Yet Mr Johnson’s main cause for hope is the unpopularity of the likely Republican and Democratic alternatives.

Around 60% of voters dislike Donald Trump and 55% Hillary Clinton. That should encourage more Americans to vote as freely of the old duopoly as they increasingly claim to be; 42% say they are independent voters, up from 30% a decade ago. And the Libertarians’ voguish message of fiscal conservatism, social liberalism and anti-interventionism has something for the disaffected of both big parties. Compared with a straightforward Trump-Clinton match-up, the Monmouth poll suggested Mr Johnson could take 6% of the vote from Mrs Clinton and 4% from Mr Trump.

The particular unease of many Republicans with their presumptive candidate—along with their failure hitherto to launch a conservative rival to him—explains a surge of interest in the Libertarian confab in Orlando. After Mr Trump sewed up their nomination in Indiana this month, Google reported a 5,000-fold increase in online searches for Mr Johnson. He is not to all Republican tastes; Mr Trump’s most outspoken critics in the party tend to hold neoconservative views on security. Yet even they hope he might bring disenchanted Republicans to the polls in November, and thereby retain their support for Republican candidates in the coterminous congressional contests.

Mr Johnson rejects Mr Trump utterly: “There’s nothing about Donald Trump that appeals to me.” Yet he sounds most hopeful of picking up support from disaffected Democrats, especially followers of Senator Bernie Sanders, whom he says he agrees with on almost everything—including the evil of crony capitalism and virtues of pot—except the economy. Yet how would he woo them?

Mr Johnson’s suggestion is unconventional. On the basis that, he argues, with some support from surveys, Americans are more libertarian than they know, he would point them to an online quiz, “Isidewith.com”, to help them work out where they stand. “I say, “Take the quiz, and whoever you pair up with, I think you should knock yourself out over them.” His own experience with the quiz, he sweetly relates, suggest he agrees with 73% of Mr Sanders’s proposals, 63% of Mrs Clinton’s and 57% of Mr Trump’s.