Javier Milei, a far-right libertarian, might soon be Argentina’s next president. He credits his cloned “four-legged children.”After finishing a surprising first in Argentina’s presidential primaries in August, Javier Milei grabbed a microphone in front of a raucous crowd and thanked Conan, Murray, Milton, Robert and Lucas.“Who else?” he said. “My four-legged children.”Mr. Milei, a far-right libertarian who is the favorite in Argentina’s presidential election on Sunday, would head to the country’s presidential offices, the Casa Rosada, not with a spouse and children, but with five mastiffs he has long called his children.He is, of course, speaking figuratively. Technically speaking, however, those five dogs are not traditional offspring of any animal. They are genetic copies of Mr. Milei’s former dog, also named Conan, and were created in a laboratory in upstate New York.Mr. Milei’s five cloned dogs have become objects of fascination in Argentina’s presidential election and a window into his unusual candidacy. For months the national debate has revolved around his ascent, his eccentric personality and his radical economic proposals — like eliminating Argentina’s central bank and replacing its currency with the U.S. dollar — to save the nation of 46 million from one of its worst financial crises in decades.Mr. Milei has made his original dog, Conan, named for the movie “Conan the Barbarian,” a central player in his back story, saying the dog saved his life and spent numerous Christmases alone with him when he felt abandoned by others.He has made the cloned dogs symbols of his libertarian ideals by naming four of them for three conservative American economists: Murray Rothbard, Milton Friedman and Robert Lucas.And at his rallies, he has held aloft paintings of his dogs, which he passes out to the crowd before picking up a roaring chain saw, his go-to metaphor for the deep cuts he wants to deliver to the Argentine government.A supporter holding a replica of a $100 bill featuring Mr. Milei with a chain saw. The tool is a symbol of the deep cuts Mr. Milei wants to make to the Argentine government.Sarah Pabst for The New York TimesMr. Milei has also signaled that cloning could find a place in his government. Last month he said that, if elected, he would appoint an Argentine scientist who has dedicated his career to cloning animals as the chairman of an influential national scientific council.“He is considered the national cloner,” Mr. Milei said of the scientist, Daniel Salamone. “This is the future.” Mr. Milei’s scientific beliefs, including denying humans’ role in climate change, have worried scientists.Mr. Milei is the front-runner in Sunday’s election, but polls suggest that he will not receive enough votes to win outright and avoid a runoff in November.Mr. Milei’s cloned dogs are also an example of a growing trend among wealthy pet owners that is raising tricky ethical questions.A handful of companies in the United States, China and South Korea have cloned hundreds of dogs since the first cloned canine in 2005. Barbra Streisand owns two clones of her Coton de Tulear, while Barry Diller and Diane von Furstenberg have three clones of their Jack Russell terriers.To clone his dogs, Mr. Milei hired PerPETuate, a company run by Ron Gillespie, 75, who got his start in the world of livestock insemination and now runs a “genetic preservation” firm from the Big Island of Hawaii.Mr. Gillespie said he received an email from Mr. Milei in 2014, saying he was interested in cloning Conan. “He said that this dog was his life,” Mr. Gillespie said.For $1,200, Mr. Milei sent a sample of Conan’s tissue to Mr. Gillespie’s business partners, scientists at Worcester Polytechnic Institute in Worcester, Mass., who used that tissue to grow cells full of Conan’s DNA and then cryogenically freeze them. (Some cells remain frozen in Worcester.)The website of PerPETuate prominently features Mr. Milei’s cloned dogs.In 2018, after Conan died, Mr. Milei reached out again. He was ready to pay the $50,000, which was the cost of a procedure that would guarantee him at least one clone.Cloning one dog usually requires more than 100 eggs — or about a year’s worth of eggs from five to 10 canines — which are surgically harvested from donor dogs, Mr. Gillespie said.Dog-cloning technology is largely the same since Dolly the sheep became the first mammal clone in 1997. Scientists remove the nucleus from each donor egg cell, wiping them clean of all their DNA. Into those empty eggs, the scientists insert the cells full of DNA of the animal being cloned.“Then we stimulate the egg cell with a shot of electricity, and that forms a one-cell embryo that immediately begins to multiply,” Mr. Gillespie said.Ten to 15 of those embryos — based fully on the DNA from the dog being cloned — are then implanted into the uterus of a surrogate dog.Some bioethicists and animal-welfare groups question the ethics of pet cloning, both for its use of animals to donate eggs and carry cloned fetuses, as well as the fact that there are already millions of unwanted pets.Jessica Pierce, a bioethicist who studies the relationship between humans and dogs, has said cloning contributes to the creation of “a canine underclass” of surrogates that live sometimes difficult lives to produce clones. “I don’t think it’s too strong to call what we do to reproductive labor dogs a form of incarceration,” she said.Pet cloning companies reject that characterization, saying many surrogate dogs are adopted by loving families.Ms. Pierce said cloning also destroys more embryos than typical dog pregnancies. She said that seemingly puts it at odds with the beliefs of Mr. Milei, who has promised to try to ban abortion because he says life begins at fertilization.Mr. Milei’s campaign declined to comment or make him available for an interview.To clone Mr. Milei’s dogs, Mr. Gillespie contracted ViaGen Pets, based outside Austin, Texas, the only American company cloning dogs. ViaGen declined to say how many eggs it used to clone Conan.ViaGen said that in nearly three out of four cases, cloning a dog produces just one clone.In Mr. Milei’s case, in 2018, it produced five.“He was ecstatic,” Mr. Gillespie said. Once the clones arrived in Argentina, one began responding to “Conan” and seemed to enjoy the same television show as Mr. Milei’s previous dog, so Mr. Milei named the clone Conan, Mr. Gillespie said Mr. Milei told him.Conan “is literally a son to me,” Mr. Milei told an Argentine news site in 2018. The other four clones “are like my grandchildren.”He also has said the dogs are a handful. “My house is like Kosovo,” he said on television in 2018. “In two weeks, they’ve eaten almost four armchairs.” Five years later, he has said the largest of the pack weighs 220 pounds.Mr. Milei’s cloned dogs are a window into his unusual candidacy — and an example of a growing trend among wealthy pet owners that is raising tricky ethical questions.Marcelo Dubini/CarasOn the campaign trail, Mr. Milei has largely kept the dogs at a day care, out of sight. But they have remained a part of the debate.Sergio Massa, Argentina’s economic minister who is polling just behind Mr. Milei in Sunday’s vote, criticized Mr. Milei’s dismissal of global warming by saying that parents are worried about the planet’s future, unlike those “who speak to their dogs like they were their kids.”Argentine news outlets have also reported that Mr. Milei has privately said that he has received strategic advice from his dogs.When asked whether he, in fact, takes advice from his dogs, Mr. Milei has remained coy.“What I do inside my house is my problem,” he told the Spanish newspaper El País. At the closing event of his campaign on Wednesday night, he called his dogs “the best strategists in the world.”Celia Melamed, an Argentine veterinarian who runs a workshop on communicating with animals, said one of her students has been Karina Milei, Mr. Milei’s sister and campaign manager.Ms. Melamed said she can feel the emotions of animals through a sort of metaphysical connection. “If I connect with an animal and it’s afraid, I feel the fear in my body,” she said. “It seems esoteric, and perhaps it is, because so far science has not dealt with this.”Mr. Gillespie, the cloning entrepreneur in Hawaii, said that since learning on Facebook that his client was a politician, he had watched Mr. Milei’s rise with fascination.“As I tell my wife,” he said, “I don’t have a vote in the Argentine election, but I do have five dogs in the race.”Lucía Cholakian Herrera More