Claims of voter fraud are common. It’s the fraud that’s rare.

In the 1941 Orson Welles epic “Citizen Kane,” newspapermen huddle near the printing press on election night as it becomes clear that the results won’t be good news for their boss, the publishing mogul Charles Foster Kane.

One of them holds up a front page with the headline they had hoped for: “Kane Elected.” He then lowers his head and nods toward the version they have to go with instead. “Fraud at Polls!” it declares.

Voter fraud is one of the oldest charges a politician can level in American elections — though no president in modern times has done so with such frequency, and so little evidence, as President Trump.

As a news story, it is sensational and often irresistible. The Brennan Center for Justice at the New York University School of Law examined its enduring appeal in a 2007 report, observing that ballot fraud has “the feel of a bank heist caper: roundly condemned but technically fascinating, and sufficiently lurid to grab and hold headlines.”

The subject’s prevalence in the conservative news media, where it is treated as a more widespread problem than the facts show, may help explain how Mr. Trump, a ravenous consumer of cable news, came to be so fixated.

In reality, elections officials across the country, representing both parties, said there was no evidence that fraud had played any role in determining the election outcome this year. The most common claims of voter fraud — reports of ballots cast by someone voting twice, or by a dead person or someone who is otherwise ineligible — can almost always be traced back to a misunderstanding like a typo, a clerical error or a false assumption that two people with a common name are actually the same person, according to the Brennan Center.

Still, the topic has been a staple of coverage on Fox News going back to the 2000s, when hosts like Bill O’Reilly spread exaggerated stories about immigrants who were voting illegally, campaigns that paid people for their votes and community groups like ACORN whose employees had submitted fraudulent voter registrations. (The ACORN employees, who were also the subject of an attack ad that John McCain’s campaign ran against Barack Obama in 2008, did not appear to be attempting to influence voting, but rather to get paid for voter registration work they hadn’t actually done.)

Claims of voter fraud have often involved absurd and far-fetched scenarios — dead people, dogs, busloads of people of color — which is another way they live on in the public imagination. In recent years, conservative activists have pushed unverified reports that buses full of illegal voters showed up at polling places from California to Wisconsin.

Famously, there was the story that Senator Christopher S. Bond, Republican of Missouri, told in 2000 about a 13-year-old springer spaniel that was registered to vote in St. Louis. Mr. Bond was making a case that more anti-fraud protections, like requiring identification, were needed after his colleague, Senator John Ashcroft, lost his seat when more Missourians voted for a dead man: Gov. Mel Carnahan, who had been killed in a plane crash several weeks before the election but remained on the ballot. Mr. Ashcroft did not challenge the results.

The fantasy of a stolen election has elements that Mr. Trump has long incorporated into his narrative about himself. There are clear perpetrators (undocumented immigrants, big-city Democratic political machines) and a victim (him) — and usually enough ambiguity so he can float outlandish but unsubstantiated rumors.

He has been laying the groundwork for refusing to concede for some time. Speaking in September to Mark Levin, the talk radio and Fox News host, Mr. Trump suggested that some voters were receiving multiple ballots in the mail. He said: “People are saying, ‘Hey, what’s going on? I just got a whole batch of ballots.’”