The most definitive answer to the future of populist nationalism could come from Britain. Boris Johnson, the likely next prime minister, has vowed a Brexit by Oct. 31, deal or no deal. His promise is a stronger, richer Britain. Yet even the most optimistic forecasts point to a serious economic hit from a no-deal Brexit.

In Greece, it did. The defeated, populist Syriza party was unable to free Greece from EU demands and end cutbacks aimed at rescuing its debt-ridden economy. In Italy, the situation is murkier. The ruling euroskeptic coalition has made little headway on ambitious economic promises. But the EU has held off imposing penalties, perhaps out of fear of the political consequences.

Two questions will determine if the populist insurgency is here to stay: whether populist movements can deliver on promises, and whether that actually matters to voters.

The resounding victory in Greece Sunday of the conservative New Democracy, the antithesis of a tub-thumping party, suggests a cautious maybe. But the jury is out in two far-larger European economic powers: Italy and Britain.

A thumping electoral turnaround in Greece – where the seeds of democratic government were first sown some 2,500 years ago – may have signaled a retreat from the mix of nationalism and populism that has been surging in key Western democracies.

But the operative word is “may.” The real significance of Sunday’s landslide defeat for the Syriza party, which rode to power promising to face down European Union fiscal conditions for rescuing Greece’s debt-ridden economy, is to highlight two questions that will determine if the wave of populist insurgency is here to stay.

The first is whether populist political movements, once in government, can deliver on their promises. The second – more intriguing, and important – is whether that will actually matter to voters, who are often motivated by a more fundamental sense that the old political system hasn’t worked for them and needs to be shaken up.

In Greece, delivering did matter. Syriza, having pledged to free the country from EU demands and end austerity cutbacks, ran into a hard reality: the risk of economic collapse. It agreed to a further EU bailout and kept austerity in place. While this helped get the economy back on its feet, voters felt betrayed. The result was the election victory of the conservative New Democracy party, led by Kyriakos Mitsotakis, son of a former prime minister and the very antithesis of a tub-thumping populist.

Now, the focus is likely to shift to a pair of far larger European economic powers in the sway of anti-EU populism: Italy and Britain. And in both, the jury is still out.

For the past year, Italy has been ruled by a coalition of two populist, euroskeptic parties: the right-wing League and the more left-leaning 5-Star. In terms of delivery, not much has been done to make good on their ambitious economic promises. Though Italy’s economy is not as precariously placed as Greece’s was, it does carry a huge public debt: around 130% of its gross domestic product. As a result, it has spent months in a game of chicken with the EU over coalition spending plans that could make the situation worse.

But Italy has more leverage than Greece does with Brussels. Its economy, the EU’s fourth-largest, is around 10 times bigger. And politically, at least part of the populist coalition seems to be thriving. The League, which began as the junior partner, turned the tables in May’s elections for the EU parliament. With its leader, Deputy Prime Minister Matteo Salvini, leading an aggressive campaign against accepting migrants and refugees, it won 34% of the vote, to 5-Star’s 17%. That was a mirror image of last year’s national election.

The EU has now stepped back from a threat to impose financial penalties on Italy for its failure to meet union budget rules – no doubt in part out of concern this might further energize Mr. Salvini’s supporters and tempt him to seek a fresh national election that would leave the League in charge.

But it’s in Britain – the EU’s second-largest economy – where the two key questions around the future of populist nationalism could get the nearest thing to a definitive answer.

After the 2016 referendum that delivered a narrow majority for leaving the EU, Conservative Prime Minister Theresa May failed to win parliamentary approval for a compromise that would have seen Britain leave while retaining some of the trade and economic benefits of being a member. She had to resign. Following a vote of party members that is now underway, she is likely to be succeeded by her former foreign secretary, Boris Johnson.

Determined to neutralize the newly formed Brexit Party, which trounced the Conservatives in the recent European Parliament elections, he has vowed to withdraw from the EU by Oct. 31 come what may, even if that means a “no-deal” Brexit with no new arrangements with Britain’s largest trade partner.

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Unless Parliament finds a way to block it, that could happen. Mr. Johnson, as a leading voice in the pro-Brexit referendum campaign, promised Britain would be stronger and ultimately richer on its own. Yet even the most optimistic forecasts point to the country taking a serious economic hit from a no-deal Brexit. In other words: promises undelivered.

Which would lead to that second question: Will it matter to voters?