Sarah Wollaston changed her mind on the EU because – unlike Britain in this debate – she cares about truth

When it’s your identity on the line, why would made-up figures about the EU be enough to change your mind?

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Poor old truth. Sarah Wollaston has done an admirable thing, switching her support for Brexit to Remain over Vote Leave’s misleading claims on health: “They have knowingly placed a financial lie at the heart of their campaign,” she writes in The Times. “Even emblazoning it on their battle bus, alongside the NHS branding, to imply a financial bonanza.”

Wollaston is smart. She calls out the falsehood without committing the debunker’s error of repeating it. But the thing about truth is, once you’re trying to establish it, the lie already has the front foot. Every time you say “not that, but this!” you’re repeating the false that and letting the honest this come second.

And so this morning, BBC Today presenter Nick Robinson challenged Leave campaigner John Redwood over the battle bus slogan…by restating the contested number six times in three and a half minutes.

Redwood only had to say it once, which must have been a relief for him given its manifest dodginess. If the politically engaged listeners to Radio 4 – blearily unsticking their eyelids, or faffing about with the kettle, or chasing their recalcitrant children out of the door to school with half an ear on the radio – remembered nothing else from that interview, they would remember this number, driven into their skulls by rote.

Not, perhaps, that it matters very much to the referendum outcome anyway. One of the most interesting bits of polling in this highly unnecessary season of politics came from Ipsos MORI, which not only asked respondents how they intended to vote, but also attempted to gauge what might change their minds.

The results suggest that Remain voters are the more classically rational crowd: given a scenario in which people would be better off by £500 after Brexit, 13 per cent switched to Leave while 41 per cent became unsure. But when Brexiters were told their preferred result would make everyone £500 worse off, only 7 per cent switched and only 32 per cent became unsure.

In other, doubtless Redwood-cheering, words: the people most likely to be influenced by hearing the battle bus figure discussed at length are the Remain voters, for whom this number acquires substance by sheer force of repetition.

Leave voters, meanwhile, are unbuyably wedded to their position. Perhaps that has less to do with idealism than cynicism. Like the Trump voters David Frum describes in an article for the Atlantic, they don’t expect to be told the truth, so the truth doesn’t matter: “What, then, was one liar more – especially if that liar were more exciting than the others”?

The £350m figure (see, it’s very hard not to repeat these things) might be a lie, but at least it’s an impressive lie. It shows commitment.

For these voters, Brexit is about something far beyond truth. It’s about an idea – an identity. They recognise something very reasonable, which is that they have limited power in their day-to-day lives.

Many of the voters who’ve given allegiance to Ukip are like those James Meek spoke to in his report from Grimsby before the 2015 election: people who had a place and power in an industrialised economy with strong unions, and have lost it. They can recognise a democratic deficit. The fact that they pin this solely on the EU perhaps says as much about the opacity of the EU as it does about the voters themselves.

The time of collective bargaining is over, until or unless participants in the new economy figure out how to organise themselves in conditions where employers deliberately impose precarity. The voice of the people is barely a whisper without institutions to act through. And the decades of brutalising war that made the European Union both necessary and possible have receded in memory to the point where it’s hard to imagine they could ever happen again.

World war is like mumps, measles and rubella: as soon as the vaccines succeeded, everyone forgot how bad the diseases were and some started wondering whether the MMR might not be a bigger problem after all.

As a population, we can’t really remember what the EU is for, and so it’s become a prop around which to suspend political identities that have become increasingly divorced from material conditions.

For Frum, Trump is a “conservative in silhouette, defined by the animosity of all the groups that revile him”. The EU is similarly a cut-out, with attitudes to it decided largely by whether you define yourself in opposition to a metropolitan elite that’s pilfered your power, or a lumpen mass of racist middle England.

The Bennite euroscepticism of Corbyn, which has shone through in every mealy-mouthed contribution he’s made to the Remain campaign he officially supports, is near impossible to understand because we no longer live in the kind of economy where it made even passing sense.

Identity politics has become a dismissive way to talk about anti-racism and feminism, but really, in the absence of any serious class analysis, all politics is identity politics now. Institutions that once supplied checks and balances are corroded; and the EU, which actually implements many of the protections workers formerly relied on collective bargaining to secure, is remote and inexplicable.

What’s left to do other than pick your side and take aim at your enemies? The EU referendum is a shadow puppet version of politics for people who are sure of very little besides their own animosities. And when it’s your identity on the line, why would a made-up £350m be enough to change your mind?

Sarah Ditum is a journalist who writes regularly for the Guardian, New Statesman and others. Her website is here.