For months, Argentina has been consumed by a single question.

Will Javier Milei — a far-right libertarian whose brash style and embrace of conspiracy theories have drawn comparisons to former President Donald J. Trump — be its next president?

On Sunday, voters will finally get to decide.

Mr. Milei, an economist and former television pundit, is facing off against Sergio Massa, Argentina’s center-left economy minister, in a runoff election. Mr. Massa led the election’s first round last month, with 37 percent to Mr. Milei’s 30 percent. But polls suggest Sunday’s race is a dead heat.

The backdrop to the contest has been Argentina’s worst economic crisis in decades, with annual inflation surpassing 140 percent, behind only Lebanon and Venezuela globally. Two in five Argentines now live in poverty. The men have offered starkly different visions on how to reverse the economic morass in the nation of 46 million — a feat that no Argentine leader has been able to accomplish for decades.

But the economic debate has been overshadowed by the rise of Mr. Milei, his eccentric personality and his radical ideas to remake the country.

With Mr. Milei now on the verge of the presidency, Sunday’s vote is a test of strength for the global far-right movement. Mr. Milei has welcomed the comparisons to Mr. Trump, as well as to Brazil’s former right-wing president, Jair Bolsonaro. And, like them, he has warned that if he loses, it may be because the election was stolen.

Here’s what you need to know about Argentina’s election.

Before Mr. Milei, 53, was a presidential candidate, he was a frontman of a Rolling Stones cover band, an economist with starkly libertarian views and a television pundit known for his fiery outbursts. In 2021, he was elected to Argentina’s Congress.

Mr. Milei has centered his campaign on an economic overhaul that would involve slashing both spending and taxes, closing Argentina’s central bank and replacing its currency with the U.S. dollar. Economists and political analysts are skeptical he would have the economic conditions or political coalition necessary to pull off such extreme change.

On the campaign trail, Mr. Milei has depicted his opponent, Mr. Massa, as the leader of a shadowy “caste” of political elites who are stealing from average Argentines — and himself as the fearless outsider who will take them on. His campaign events depict him as a roaring lion as his supporters chant, “The caste is afraid.”

Yet his eccentric personality and pugnacious politics have often attracted the most attention. There have been his harsh attacks against the pope, his clashes with Taylor Swift fans, his claims of being a tantric-sex guru, his assertion that climate change is a socialist plot, his dressing up as a libertarian superhero and his close relationship with his Mastiff dogs that are named for conservative economists — and are also all clones.

Mr. Massa, 51, has spent his entire career in politics, including as a mayor, congressman and a cabinet chief to a president, swinging from the right to the left and earning a reputation as a pragmatist.

That is the same approach he has taken during the presidential campaign, touting his ability to run the government, work with industry and build a political coalition to fix the economy.

But to many Argentines, he has little credibility on economic matters. He has overseen Argentina’s economy for the past 16 months, just as it has cratered. Inflation has soared, and the value of the Argentine peso has plummeted. In July 2022, when Mr. Massa was appointed economy minister, $1 bought about 300 pesos on the main unofficial market. Now $1 buys 950 pesos.

Argentina’s woes hardly began with Mr. Massa. For decades, failed economic policies, including high government spending and a protectionist approach to trade, have left Argentina with one of the world’s most perpetually unstable economies, despite its abundant natural resources.

Mr. Massa blamed a record drought and $44 billion in international debt for hurting so many Argentines during his run as economy minister. “We lost half of our agricultural exports” as a result of the drought, he said in an interview, “so the main challenge was to sustain the level of activity and employment.”

Argentina’s economy shrank by 4.9 percent in the second quarter of this year, the latest data available, the first decline after nine consecutive quarters of growth, in which the country rebounded from the pandemic. Unemployment has also mostly fallen in recent quarters, down to 6.2 percent by the end of June.

Mr. Milei’s platform is centered on his pledges to close the central bank and dollarize the economy. During the campaign, Mr. Milei would smash miniature versions of the central bank and hold aloft giant $100 bills with his face on it.

Mr. Milei also had another campaign prop: a chain saw that he would wave around at rallies. The saw represented the deep cuts he is proposing to government, including lowering taxes; slashing regulations; privatizing state industries; reducing the number of federal ministries to eight from 18; shifting public education to a voucher-based system and public health care to insurance-based; and cutting federal spending by up to 15 percent of Argentina’s gross domestic product. He has recently softened some proposals after blowback.

He also has said he would like to ban abortion, loosen gun regulations and largely cut relations with any country beside the United States and Israel.

In an interview, Mr. Massa called Mr. Milei’s proposals “suicidal” for the country.

His plans for change are far more modest. Mr. Massa said he wants to increase production of oil, gas and lithium; simplify the tax system; and reduce overall spending while increasing spending on education and job training. “Austerity,” he said.

His calls for austerity, however, have been undercut by his moves in recent months to cut taxes, give bonuses to workers and release more money to the poor. Critics have called the policies irresponsible patronage during an economic crisis.

For months, Mr. Milei has claimed, without evidence, that he was robbed of more than a million votes in a primary election in August, or 5 percent of the total. He has also said that the first round of the general election last month was rigged against him.

He has argued that fraudsters are stealing and damaging his ballots at polling stations, preventing his supporters from voting for him. (In Argentina, citizens vote by inserting a paper ballot of their preferred candidate into an envelope and dropping the sealed envelope into a box. Campaigns distribute ballots with their candidate’s name to polling stations.)

Election officials dispute Mr. Milei’s claims, and his campaign has offered little evidence. His campaign’s legal director said in an interview that he had direct knowledge of only 10 to 15 written complaints from voters.

This past week, Mr. Milei’s campaign escalated its fight, filing a document with a federal judge that claimed “colossal fraud,” asserting that Argentine officials changed votes for Mr. Milei to Mr. Massa. The campaign cited anonymous sources.

Mr. Milei has openly questioned the results of the 2020 U.S. election and the 2022 Brazil election, which were dogged by baseless claims of fraud that led to violent attacks on those nations’ capitols.

Now, Argentines are bracing for what could happen if Mr. Milei loses. His supporters have called for protests outside the election agency’s headquarters after the polls close on Sunday.

On Friday, Mr. Milei said Mr. Massa’s incumbent party “is showing very rude signs of desperation” and would most likely try to cling to power if Mr. Milei wins. In that scenario, he added, his government “will apply justice with all due force.”

Lucía Cholakian Herrera and Natalie Alcoba contributed reporting.

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