Do gamblers know something that pollsters do not? Ever since the Liberal Democrats’ record European election result and the arrival of their new leader, Jo Swinson, there’s been a spring in their step. Polls show the Lib Dems nipping at Labour’s heels. A victory in the Brecon and Radnorshire byelection and then the defection of half a dozen MPs from rivals in recent weeks has helped to attract a record membership. The party is now hoping to be swollen by an influx of radicalised remainers, attracted by the party’s decision to change its approach to Brexit. Lib Dems no longer want a second Brexit referendum; instead they would simply revoke article 50 without a public vote. This policy will only become law if the Lib Dems win a parliamentary majority, a possibility which the betting markets think has as little as a 5% chance. The party appears not to be serious about power, offering an empty pledge that is impossible to redeem.

Ms Swinson’s wager appears to be that she is right and the punters are wrong. In the Brexit referendum there was a tendency to underestimate the appeal of leave, and the Lib Dems think Westminster is now ignoring the latent remain vote. It is true that a petition supporting the revocation of article 50, which would stop Brexit in its tracks, attracted more than 6m signatures. It is also the case that Brexit is likely to feature as a big issue in the next general election, and the Lib Dems see an advantage in carving a niche out of make-it-stop politics.

The most obvious problem with this approach is that recent history suggests it takes a referendum to overturn a referendum. Ireland was the only country to submit the European Union’s Lisbon treaty to a plebiscite. In 2008 Irish politicians failed to convince the voters, who voted no by a margin of 53% to 46%. Sound familiar? The more educated voted yes and the least educated voted no. Among manual workers, three-quarters voted no. A year later, Irish voters thought better of the result, with two-thirds voting in favour of the Lisbon treaty.

The winner-takes-all mentality behind Ms Swinson’s policy is troubling. The lack of a democratic mandate for revoke means it could entrench a permanent divide in British life that will be impossible to bridge. Politicians ought to think about their policy’s consequences. If the Lib Dems’ idea is accepted, then why couldn’t the SNP be permitted to hold a second independence vote if it won the next Holyrood election? Then there are the accusations of inconsistency. In 2008 Ms Swinson wanted a referendum on EU membership. Two years later she campaigned on a manifesto that committed the Lib Dems to an in/out EU referendum. She was a minister in an austerity government that did so much to create the pain and division behind the leave howl. In 2016 an EU referendum took place. The country voted out. Three years later, Ms Swinson won’t accept the outcome of a plebiscite she had said she wanted.

The Lib Dems are positioning themselves to tap future popular revulsion against the major parties. Yet the politics of protest only works if there is something to protest about. If Boris Johnson strikes a Brexit deal with the EU, where does this leave Ms Swinson? The Lib Dem policy also gives Labour a clear run at a second referendum. Ms Swinson’s offer is just to permanently polarise the electorate around Brexit. The Lib Dems still have no distinctive pitch for issues beyond leaving the EU. This is the party of ideas, home to Keynes and Beveridge. But there’s no sign of a middle way being plotted by the party between the extremes. Unless Ms Swinson can do so, the odds will be stacked against the Lib Dems in a general election.