Yes, there are lessons for U.S. politics in the landslide victory of British Prime Minister Boris Johnson’s Conservative Party and the historic collapse of Jeremy Corbyn’s Labour Party. But watch out for precooked conclusions based on ideological predispositions, and pay attention to the ways in which Britain’s situation is very different from our own.

In a sign of how transnational politics has become, debates that broke out in Britain as soon as the breadth of Thursday’s Tory landslide became clear were quickly replicated on our side of the Atlantic.

Within Labour, two camps formed almost instantly: “Blame Brexit” from the left vs. “Blame Corbyn” from the center and center-left. Thanks to social media, competing wings of the Democratic Party joined the fray.

Defenders of Corbyn and his left-wing policies said the election was all about Johnson’s success in making Britain’s withdrawal from the European Union the campaign’s overriding issue. In this view, Labour was crushed in its working-class heartlands in northern England and the Midlands because previously faithful voters embraced Johnson’s core promise to “get Brexit done.”

By contrast, Labour and Corbyn offered a soggy position aimed at uniting the party’s anti-Europe voters in the old factory and mining areas with Europe’s supporters, especially in London and Scotland. Corbyn said he would negotiate a better withdrawal agreement and then put it to a new referendum.

It didn’t sell, and both working-class and left-wing Labourites (they’re not necessarily the same) blamed posh Labourites in southern England for saddling the party with a position it could never sell in areas that had voted overwhelmingly to leave the E.U. “It’s not Jeremy Corbyn,” insisted Ian Lavery, the Labour Party chairman. “It’s Brexit.” Corbyn himself argued that Brexit “has overridden so much of a normal political debate.”

Nonsense, said Corbyn’s critics. Polls showed that two to three times as many voters disapproved of Corbyn as approved of him. “Every door I knocked on, and my team and I spoke to 11,000 people, mentioned Corbyn,” tweeted Ian Murray, a Labour MP from Edinburgh who survived the deluge. “Not Brexit but Corbyn.” Middle-of-the-road former Labour adviser Ayesha Hazarika told the BBC: “Corbynism has been tested to destruction.”

What do the data say? Brexit was, indeed, a huge problem for Labour, but so was Corbyn. A BBC analysis found that in constituencies that voted strongly to leave the European Union, the Labour vote was down by 10.4 percent while the Conservative vote was up by 6.1 percent. Case closed? No. In areas that voted strongly to remain in the E.U., Labour’s vote was also down, by 6.4 percent, while the Conservative vote dropped by 2.9 percent. The pro-remain areas shifted toward the passionately pro-remain Liberal Democrats, but not by enough to save the party from a disaster of its own.

Corbyn, in short, hurt the party almost everywhere.

His resounding defeat — Labour will have the fewest parliamentary seats since 1935 — does not mean that the candidacies of Sens. Elizabeth Warren (D-Mass.) or Bernie Sanders (I-Vt.) are automatically doomed. Corbyn is well to the left of both and had problems of his own (including his deeply flawed response to an outbreak of anti-Semitism in his party). But the Labour leader’s showing is a cautionary tale. It’s hard to argue now, as some on the left once did, that Corbynism represents the wave of the future.

If the left/center-left split is real, so is the divide between bustling cities and the places that Michael Gove, an influential Conservative, called “overlooked and undervalued.” Political scientist Matthew Goodwin argued that Labour is now split in three: a “liberal degree-holding Brahmin Left,” a “dwindling blue-collar, socially conservative Traditional Left,” and “students” plus “ethnic minorities.” These dividing lines will also be familiar to Americans.

Whether Johnson lives up to his promises or not, it’s worth remembering that in seeking working-class votes, he moved his party to the left on economics by promising more spending on health services and infrastructure. There may be a lesson here for the hyper-ideological conservatives in the United States.

As for the European Union, the great paradox is that what looks like a Brexit landslide is nothing of the sort. Taken together, the pro-leave parties — the Conservatives and the Brexit Party — received about 46 percent of the vote. Labour, the Liberal Democrats, the pro-E.U. Scottish National Party (which swept Scotland) and the Greens won about 50 percent.

Johnson outplayed Europe’s fractured supporters ruthlessly and brilliantly. He has yet to convince his country that the course he is about to embark on is right.

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