In the same election, accusations of voter fraud became a volatile issue in Missouri. Republicans claimed that Democrats in St. Louis were trying to steal that state’s Senate election after lawyers for Al Gore’s campaign won a court order keeping the city’s polls open late to accommodate voters who had been wrongly removed from the rolls.
And issues of race, often a subtext in Republican charges of fraud, were accentuated by the election of the nation’s first black president in 2008. Republicans accusations of voter fraud, as in St. Louis, have frequently been directed at minority groups in cities such as Philadelphia and Chicago. The issue now thrives in the hothouse of the internet, where corrections of fact and debunkings rarely catch up with the claims they address.
Mr. Trump’s pronouncement “did not come out of thin air,” Richard L. Hasen, an election law expert and professor at the University of California, Irvine, said in an interview. “It is, in fact, an often-repeated theme by those on the right who have been claiming, especially since 2000, that Democrats are stealing elections with voter fraud.”
The notion of widespread fraud has also become a potent political weapon: Since 2010, 16 states have placed new identification requirements on voting in the name of security. Increasingly, they have required voters to produce proof of identification that young, poor and minority voters — often Democrats — disproportionately lack.
None of that is to say that American elections are flawless. On the contrary, the national election system is a hodgepodge of outdated voting machines, underfinanced election offices and voter registration lists riddled with errors and insufficiently groomed to remove the dead and people who have moved away. And experts say a new and growing worry is the possibility of the hacking of election rolls, including by foreign interests.
A 2014 report in the journal Electoral Studies — roundly criticized by other researchers as methodologically flawed — suggested that registration procedures are lax enough that as many as one in 15 non-United States citizens living in the country could have mistakenly cast ballots in the 2008 election. A 2012 study by the Pew Center on the States, cited by Mr. Trump on the campaign trail, concluded that 24 million registrations were outdated or invalid, 1.8 million registrants were dead and 2.75 million were registered in more than one state.
But even the study that Mr. Trump cited pointed to inefficient administration, not fraud. It said there was no evidence of noncitizen voter registration or voting, and no evidence of voter fraud due to out-of-date records or deceased people still on voting rolls. Officials say voter rolls are more accurate now than when the study was done in 2012.
And, perhaps most important, the principal fraud that Mr. Trump and most Republicans assail, and the only one that voter identification laws address — voters who intentionally misrepresent themselves at polling places — is exceedingly rare, experts say. They add that it is almost impossible to perpetrate on a scale that would affect the results of a national election. Democrats also note that with Republican domination of state governments, voting nationwide is increasingly overseen by Republicans.
No national database of voter fraud cases exists. But a study by Justin Levitt, a professor at Loyola Law School in Los Angeles who currently works in the Civil Rights Division of the Justice Department, uncovered only 31 credible claims of voter impersonation between 2000 and 2014, out of one billion ballots that were cast. An Arizona State University journalism project reviewed 2,068 allegations of election fraud between 2000 and 2012 and concluded that only 10 had involved misrepresentation.
More common and largely unaddressed, but still rare, are fraudulent mail-in ballots and corruption among election officials.
Fraud charges are a staple of American politics, and once were frequently true. Terre Haute, Ind., was infamous for a 1914 scandal in which the mayor rigged voting machines, bought off voters, registered thousands of nonexistent voters and arrested nosy poll watchers.
But if thievery has not vanished since then, its scope has shrunk markedly: Four Troy, N.Y., officials and party workers were convicted in 2011 for creating false absentee ballots that may have swung local elections. And the next year, Indiana’s chief elections official, Secretary of State Charlie White, was convicted of six felonies involving voter fraud, including submitting a false ballot.
The possibility that fraud or incompetence could change the outcome of a close presidential contest, as some claim happened when John F. Kennedy took the White House on the strength of an 8,000-vote margin in Illinois, is at least conceivable, experts say. But even other Republicans have scoffed at Mr. Trump’s claims this year’s election could be rigged by voter fraud. Gov. John Kasich of Ohio, a Republican primary foe, likened them on Wednesday to “saying we never landed on the moon, frankly. That’s how silly it is.”
Yet the charges by Republicans that fraud is pervasive have grown in the last 15 years, driven both by the party’s rightward shift and by national events.
Since the 2000 presidential election underscored the crucial role of voting rules in close races, allegations of widespread fraud also have figured in high-stakes political strategies. Increasingly, voter identification laws and other restrictions advertised as election security measures help determine who votes, and who does not.
“Suddenly, it became clear that in very close elections, manipulating the rules could potentially matter,” said Mr. Hasen, the election law expert. “And so voter fraud became an excuse for making it harder to register and to vote.”
And as the notion of pervasive fraud gained political value, keeping it in the public eye became smart politics as well.
During the administration of George W. Bush, Attorney General Alberto R. Gonzales, a Republican, directed United States attorneys to aggressively pursue voter-fraud cases after Mr. Bush and his political adviser, Karl Rove, called for a focus on the issue. By 2007, five years after the fraud crackdown began, the attorneys had brought just 120 cases nationwide — many involving mistakes or petty violations like completing more than one registration form — and won 86 convictions out of about 200 million votes cast.
Mr. Obama’s general-election opponent in 2008, Senator John McCain, savaged him over allegations of voter-registration fraud by a left-leaning neighborhood organizing group, the Association of Community Organizations for Reform Now, or Acorn, that had run registration drives in 21 states. Mr. McCain said Acorn was “on the verge of maybe perpetrating one of the greatest frauds in voter history in this country, maybe destroying the fabric of democracy.”
Republicans accused Acorn’s voter-registration workers of falsely enrolling voters on a vast scale, sometimes with names like Mickey Mouse. Some workers did submit false registrations, but the group said it regularly worked to detect such fraud and fired those involved. A 2009 inquiry by the Congressional Research Service found no evidence that anyone registered by the group had cast a fraudulent ballot.
Investigations suggested that the group’s greatest crime may have been sloppiness, not intended fraud. But the charges added to a snowballing public conviction that fraud is rife. Nearly half of Americans believe voter fraud happens at least somewhat often, and 70 percent think it happens at least occasionally, according to an ABC News/Washington Post poll released last month.
Then and now, Republican leaders have said repeatedly that the requirements are sorely needed to rein in ballot-box misrepresentation, largely by Democrats. “Leaders of the other party are against efforts to crack down on voter fraud,” Gov. Greg Abbott of Texas, a Republican, said in March. “The fact is that voter fraud is rampant.”
Among many Republicans, fraud’s ubiquity remains evident. “There are instances all over southeast Missouri,” said former Senator Kit Bond, one of those who raised accusations of fraud in the St. Louis voting in 2000 and now a St. Louis lawyer. “A lot of people tell tales of buses being loaded up and visiting numerous polling places. And there’s some instances this year. It’s a small percentage that we discover.”
But few of the claims have been confirmed.
After investigations of the alleged fraud in St. Louis, only six of the 2,361,586 Missouri votes cast in the 2000 election were conclusively found to have been ineligible, either deliberately or inadvertently.
The Kansas secretary of state Kris Kobach — a Republican, self-proclaimed Trump adviser and ardent advocate of a voter-fraud crackdown — asserted in an interview this year that he had uncovered a score of foreigners in just one Kansas county who had illegally registered to vote or had been stopped from registering. A list of the 17 noncitizens cited in a federal lawsuit showed that only one had ever cast a ballot; five had notified authorities of erroneous registrations on their own or through relatives.
In Lee County, Fla., a 2012 television news report that claimed to find over 100 foreigners illegally registered to vote prompted a criminal inquiry and cries for reform. But while officials did uncover some wrongly enrolled foreigners, few had actually voted, and error or confusion, not fraud, was the culprit, the county supervisor of elections, Sharon L. Harrington, said.
“There has never been any prosecution in Lee County of anyone who registered and/ or voted illegally, even though information has been submitted to our state’s attorney’s office,” she said in an email. “This is not a widespread issue.”
A conservative advocacy group made headlines in 2014 when, days before the November election, it filed a lawsuit alleging that thousands of Frederick County, Md., voters were actually illegally registered foreigners. But the suit was withdrawn two weeks later after the headlines faded. Maryland’s chief investigator of election corruption, James Cabezas, said the allegations were unsubstantiated. “Whoever’s saying all these people falsely voted, that they’re illegals, that’s just not true,” he said.
Indeed, most voting experts say threats of voters being disenfranchised are far more worrisome than widespread fraud.
“The frame is being controlled here by those who are promoting the idea that fraud is the problem,” said Lorraine Minnite, a Rutgers University professor of political science and author of the book “The Myth of Voter Fraud.”
“If we shifted the framework to people who are trying to vote but don’t get their votes counted,” she said, “we’d be having a different discussion.”
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