2. Stronger voting procedures generally means voter ID laws aimed at in-person voting fraud. Those laws disproportionately affect the poor, the elderly and people of color — groups that often overlap with Democratic voters.

3. A study from the nonpartisan Government Accountability Office found that new voter ID laws in Kansas and Tennessee reduced the total vote in those states in 2012 by 100,000 votes. Most affected? Young people, black people and newly registered voters.

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4. Trump began talking about the possibility of the 2016 election being affected by voter fraud before the election even happened. At the time he first mentioned it, in Pennsylvania in early October, he trailed Hillary Clinton both nationally and in that state. He told an audience that the only way he would lose Pennsylvania was if fraud occurred.

5. He won Pennsylvania.

6. In fact, Pennsylvania itself tried to crack down on voter fraud under a previous Republican governor. In defense of a law implemented before the 2012 election, the state filed a brief with the court acknowledging that there “have been no investigations or prosecutions of in-person voter fraud in Pennsylvania; and the parties do not have direct personal knowledge of any such investigations or prosecutions in other states.”

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7. This shouldn’t come as a surprise. Multiple investigations of the extent of in-person voter fraud — someone showing up to vote fraudulently — have found that it’s not a significant problem.

8. One study found 31 credible incidents of fraud out of 1 billion votes cast over a decade nationally.

9. Last year, given the attention being paid to fraud by a major-party candidate, research was done to evaluate the extent of fraud in the 2016 election.

10. Researchers from Dartmouth looked for statistical fingerprints of fraud, comparing vote totals to county deaths and noncitizen populations. They found no evidence that either noncitizens or the dead were casting illegal votes.

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11. The report put it bluntly: “Voter fraud concerns fomented by the Trump campaign are not grounded in any observable features of the 2016 presidential election.”

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12. Those two possibilities — voting by noncitizens or the dead — have been highlighted in the past by Trump as evidence of rampant fraud, and are the two examples he uses in his tweets.

13. Those who claim that noncitizens vote regularly often point to a study that purported to show that 14 percent of noncitizens in the United States were registered to vote. That study was thoroughly rebutted last year. The apparent voting was, it seems, a function of errors in measurement.

14. Claims that millions of people voted illegally in the 2016 election are largely rooted in one tweet from one guy who made the claim shortly after Election Day. He has offered no evidence to support the claim, and a voter protection organization with which he’s affiliated has declined to do so as well.

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15. The dead-people-voting idea is one rooted in the popular imagination, certainly, but those who argue that it’s a rampant problem usually point to a 2012 study from Pew Trusts pointing out that the nation’s voter rolls are often out-of-date and include hundreds of thousands of dead people.

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16. Which is not to say that 1) those registrations are used to cast votes or 2) that they were used to cast votes in the 2016 election. After Trump began hammering this drum, one of the authors of the study stated explicitly that there was “zero evidence of fraud” in this election.

17. That’s not exactly true. We looked for media reports of fraud after the election and found that it did exist.

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18. We found four incidents.

19. Two of the four were Trump voters, who cited Trump’s claims of fraud as their excuse. One was not a federal election. One was a Republican election judge who cast a ballot for her dead husband.

20. The National Association of Secretaries of State — an organization of the elected officials responsible for conducting elections at the state level — released a statement saying that it was “not aware of any evidence that supports the voter fraud claims made by President Trump.”

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21. The majority of those secretaries of state, by the way, are Republican.

22. Another significant body argued in a legal briefing that the 2016 election was free from significant fraud: the Trump campaign.

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23. In a response to efforts to recount ballots in Michigan, Trump’s lawyers wrote that “all available evidence suggests that the 2016 general election was not tainted by fraud or mistake.”

24. A presidential investigation into voter fraud has been conducted before. George W. Bush enacted one when he was president. After five years of looking, it found “virtually no evidence of any organized effort to skew federal elections,” in the words of the New York Times.

25. Trump’s press secretary said Tuesday that Trump believed in voter fraud in the 2016 election because of “studies and evidence.” Those have not been presented, nor have any observers seen them.

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26. That Trump focuses on the possibility of 3 million fraudulent ballots indicates another motivation for his raising the issue: His 2.9 million vote loss to Hillary Clinton. There may, in other words, be a personal political motivation for making these claims.

27. The last time Trump embarked on a thorough investigation, it was for personal political purposes.