On Sunday, President-elect Donald Trump set off a political firestorm when he claimed, in a series of tweets, that he lost the popular vote to Democrat Hillary Clinton because “millions” of people voted illegally in the 2016 election.

In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally — Donald J. Trump (@realDonaldTrump) November 27, 2016

Mr. Trump’s argument -- which came in the wake of a three-state recount effort initiated by Green Party candidate Jill Stein -- has been debunked by fact-checkers across the internet, including Politifact (which rated his claims “Pants on Fire”), the Washington Post’s Fact Checker blog and Snopes.

“Simply put, there is no evidence that “millions of people” voted illegally in the election,” the Post’s Glenn Kessler wrote.

So where is Mr. Trump getting his information?

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Trump’s sources

Asked about this issue on the daily transition call, Trump transition spokesman Jason Miller cited two sources for Mr. Trump’s claims: a 2014 Washington Post article about non-citizen voting, and a 2012 Pew Research Center study that said one in eight voter registrations in the U.S. are no longer valid.

“So all of these are studies and examples of where there have been issues of both voter fraud and illegal immigrants voting,” he said. “So if this much attention and oxygen is going to be given to complete frivolous, throw away fundraising scheme[s] by someone like Jill Stein, then there should be actual substantive looks at the overall examples of voter fraud, illegal immigrants voting in recent years.”

This isn’t the first time both the 2014 Post story and the 2012 Pew study have gotten a mention this election cycle: back before Election Day, when Mr. Trump was warning his rallies of widespread voter fraud, these were the two stories he cited. Both were criticized at the time as insufficient proof.

The 2014 Washington Post study

The Washington Post study he refers to, published in an October 2014 article titled “Could non-citizens decide the November election,” was not actually conducted by the newspaper -- it was a guest post by two professors from Old Dominion University who had just written a scholarly article on the topic.

The two professors, Jesse Richman and David Earnest, used figures from the Cooperative Congressional Election Study (CCES) in 2008 and 2010 to suggest that non-citizen voting is more widespread than people think. According to their research, 14 percent of non-citizens said in the survey data that they were registered to vote.

However, the Post article was roundly criticized -- and Richman’s and Earnest’s methodology appeared to be dubious enough that the Post affixed a note at the top the article saying another article claimed the study’s findings “were biased and that the authors’ data do not provide evidence of non-citizen voting.” The story was also published more than two years ago, and thus, it makes no claims about specific instances of non-citizen voting in 2016.

The 2012 Pew study

As for the second source Miller cited, the 2012 Pew study, the study found that approximately 24 million voter registrations, or roughly one in eight, are either inaccurate no longer valid. Additionally, the study said 1.8 dead people are still listed as voters, and 2.75 million people are registered in more than one state.

One of the authors of the Pew study, David Becker, tweeted Monday that Mr. Trump and his team were misrepresenting the findings of the study, though: while it did prove that the voter rolls contain names they shouldn’t, their study included no concrete findings or conclusions about voter fraud.”

“As primary author of the report the Trump camp cited today, I can confirm that report made no findings re: voter fraud,” Becker tweeted.

Three million?

There is a claim that three million undocumented immigrants voted illegally in 2016. This appears to have been originally published on InfoWars.com, the website run by radio host and conspiracy theorist Alex Jones.

The three million figure seems to have originated with a Republican self-described voter fraud expert, Gregg Phillips, whose Twitter bio says he works for an organization called VoteFraud.org.

However, VoteFraud.org redirects to a website at the URL electionnightgatekeepers.com, which contains no evidence relating to non-citizen voting. Shen journalists began asking Phillips for his data, he said it was still being analyzed -- and he declined to make any information or evidence available.

“No. We will release it in open form to the American people,” he responded on Twitter to one reporter. “We won’t allow the media to spin this first. Sorry.”

Election officials’ responses

For their part, government and election officials have all denied that there is any issue with widespread non-citizen voting.

In another tweet Sunday, Mr. Trump suggested voter fraud had occurred in three states that he lost: California, New Hampshire and Virginia:

Serious voter fraud in Virginia, New Hampshire and California - so why isn't the media reporting on this? Serious bias - big problem! — Donald J. Trump (@realDonaldTrump) November 28, 2016

Officials in all three states disputed Mr. Trump’s claims, saying there was no evidence whatsoever of widespread voter fraud. In California, Secretary of State Alex Padilla said Mr. Trump’s accusation are “absurd.”

“It appears that Mr. Trump is troubled by the fact that a growing majority of Americans did not vote for him,” Padilla said in a statement Sunday night. “His unsubstantiated allegations of voter fraud in California and elsewhere are absurd. His reckless tweets are inappropriate and unbecoming of a President-elect.”

In New Hampshire, Senior Deputy Secretary of State David M. Scanlan, who runs the state’s Election Division, said their office had received a small number of complaints but nothing beyond the usual number they get in an election cycle.

“There’s no indication of anything that widespread taking place in New Hampshire,” he said, according to the New Hampshire Union Leader. “If he has evidence he should pass it along so we can act on it.”

And in Virginia, Gov. Terry McAuliffe said there was no reported voter fraud in the state and that Mr. Trump should “put proof behind” his allegations.

White House Press Secretary Josh Earnest, too, said in Monday’s press briefing that there has been “no evidence produced to substantiate” Mr. Trump’s claim.

“I think there is a difference between unfounded claims of fraud and a conscientious interpretation of the recount law that is consistent with the rules that Democrats and Republicans alike apply in a situation where there’s a narrow victory by one candidate or the other,” he said.