The accusation arose Thursday morning, when Shawn Jasper, the speaker of New Hampshire’s Republican-run House of Representatives, released data on same-day registrants that he’d obtained from the secretary of state’s office. In November 2016, 6,540 voters had registered to vote on Election Day. As of Aug. 30, just 1,014 of those voters had obtained a New Hampshire drivers license. A few hundred voters did not obtain state licenses but had registered cars in the state.

That was enough for Jasper to allege thousands of fraudulent votes — and for Kansas Secretary of State Kris Kobach, the vice chairman of the commission, to flatly allege that fraudulent voters might have stolen the state’s four electoral votes and a U.S. Senate seat away from Republicans.

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“If 59.2 percent or more of them went for [Democratic Sen. Maggie] Hassan, then the election was stolen through voter fraud,” Kobach wrote in a column for Breitbart. “That’s likely, since the surrounding states are Democrat (sic) strongholds.”

Kobach apparently made no attempt to contact voters who’d cast ballots but held out-of-state IDs. Thursday night, The Washington Post asked voters who’d done so to tell their stories; three did so within 60 minutes — college students, who were living in New Hampshire but did not change their licenses.

Patrick Derenze, 22, said that he voted with a New York ID, and was unaware of any New Hampshire law that required voters to change their licenses after voting.

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“I was a student at Saint Anselm College in Manchester until I graduated this past May, and because I spent most of my time in the state I felt it was right I vote there instead of my native state of New York,” Derenze said.

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Alexander J. Rounaghi, 19, used his California ID to vote while studying at Dartmouth. “I lived in New Hampshire then, and I’ll live there again when I’m back from summer vacation,” he explained.

Jonah Cohen, 20, was also studying at Dartmouth when he used his New York ID to vote in New Hampshire’s 2016 election. “I’ve since transferred to Columbia, so I won’t be voting in New Hampshire anymore, but I haven’t changed my registration yet,” he explained. “I did not end up getting a N.H. license, but I never needed one to vote.”

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It’s possible that thousands of other New Hampshire college students voted the same way; the ability of temporary residents to swing close elections has been controversial in the state for years, as Democrats go through the same biennial battle to drive up turnout on campuses.

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“Apparently, Kobach is saying that voting should be limited to people who drive cars,” said David Becker, director of the Center for Election Innovation. “He’s basically saying Bill Gardner, New Hampshire’s secretary of state — his colleague — is incompetent. And he’s doing it without a basis.”

But Kobach was only the most prominent commission member mangling the data. J. Christian Adams, a commission member who has sometimes accused voters of fraud based on badly flawed data, wrote Thursday that the 5,000-plus voters who had voted in 2016 but had not switched their IDs could “no longer be found in New Hampshire.”

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That was false: Even the chair of Dartmouth’s College Democrats, Jennifer West, said Thursday that she held an out-of-state ID while studying and organizing voters in New Hampshire.