But here’s a similarity that few have noticed: In advance of the poll, both campaigns have claimed that the votes would be riddled with flaws. Their supporters also planned to intervene in the electoral process and stop the “fraud.”

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The Brexiteers warned that the referendum would be rigged and that ineligible immigrants would vote

Trump has been claiming, without evidence, that the vote will be rigged against him and has called on his supporters to monitor the polls. Several Brexit campaigners did the same — including United Kingdom Independence Party leader Nigel Farage, now a Trump supporter.

Such tactics weren’t new for Farage’s team, which alleged fraud when he lost his 2015 race for a seat in Parliament from Thanet South.

As the Brexit referendum approached, Farage was keen to point out that ineligible “E.U. migrants” were being sent poll cards.

There was then an organized Brexiteer campaign to have voters take their own pens to the polling stations. If citizens used the pencil provided by electoral officials, they warned, their votes could be rubbed out and changed. The hashtag #Pencilgate was born. One poll found that more than half of “Leave” voters thought that the referendum would be rigged.

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More was to follow. Just as the polls closed and before the result was known, Farage argued that the government’s late extension of the voter registration deadline had “got 2 million voters . . . [and] tipped the balance” in favor of the “Remain” campaign. The extension occurred because the government’s central electoral registration website crashed just before the original deadline. Last-minute legislation added 48 hours to the deadline.

But we found no evidence of electoral irregularities

Trump’s claims about U.S. voter fraud have been repeatedly exposed as baseless. Similarly, my recent research with Alistair Clark show that this type of voting irregularity are scarcely a problem Britain’s referendum. The problems with the electoral machinery lie elsewhere.

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At last year’s general election, we surveyed poll workers about the challenges they faced running the election. Poll workers at British elections are mostly a mix of local government employees and civic-minded volunteers, often retired, who are paid a small fee for the day.

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They reported that a common challenge was unregistered voters showing up at the polls, expecting to vote. Two-thirds of polling stations turned away at least one citizen, presumably because they were missing from the electoral register. Millions of people are missing from the electoral register in Britain, as a U.K. parliamentary group has pointed out. But fewer than 1 percent of poll workers suspected electoral fraud might have taken place in their polling station (see Table 2 of the chapter).

During the Brexit referendum, we conducted a second study in which we surveyed and interviewed middle-management electoral officials. The research was published in an independent report, conducted for and funded by the Electoral Commission, the organization charged with overseeing the referendum.

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All told, 382 independent nonpartisan local organizations were involved in delivering the survey. That made a coordinated conspiracy in their replies implausible. Respondents were ensured that their responses would be confidential so that concerns could be raised, if they were held. While no method is perfect, the data provided the most systematic picture yet of the quality of the British electoral machinery.

Again, few mentioned electoral fraud as a problem. Some inexperienced election agents needed to be educated about the “dos” and “don’ts.” #Pencilgate was only a challenge when voters threw pens, as they did at some polling officials. But few suspected voter fraud by mail, electoral fraud or voters impersonating someone else in order to vote more than once.

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Many electoral officials, by contrast, were concerned about the capacity of their teams to ensure that legitimate citizens were able to vote. They faced a public confused about whether they were already registered and were bogged down by large number of duplicate applications (see tables 1 and 2 of the report). Legitimate would-be voters were again turned away from the polls (Table 10), sometimes because they had been removed as a result of recent government reforms to “clean up” the register and prevent electoral fraud.

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Most said that they didn’t have enough funds to undertake core tasks (see Table 7 of the report). These are problems which are often reported in the United States, too.

Baseless claims of voter fraud have a long history

Trump, of course, is not the first American politician to invoke voter fraud for political ends. U.S. history is steeped with politicians claiming widespread election fraud to justify measures that might keep voters who lean toward the other party away from the polls.

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Indeed, the Brexiteers may well have been aware of this tradition when employing their own tactics earlier in the year.