By Aaron Blake | Washington Post

President Donald Trump has said repeatedly that Russian interference didn’t matter in the 2016 election, and he has suggested – wrongly – that the intelligence and law enforcement communities have said the same. His overriding fear seems to be that Russian interference and the “fake news” it promoted would undermine the legitimacy of his election win.

Trump won’t like this new study one bit.

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The study from researchers at Ohio State University finds that fake news likely played a significant role in depressing Hillary Clinton’s support on Election Day 2016. The study, which has not been peer reviewed but which may be the first look at how fake news impacted voter choices, suggests that roughly 4 percent of former President Barack Obama’s 2012 supporters were dissuaded from voting for Clinton in 2016 by belief in fake-news stories.

Richard Gunther, Paul Beck and Erik Nisbet, the study’s authors, inserted three popular fake-news stories from the 2016 campaign into a massive, 281-question YouGov survey given to 585 Obama supporters in December 2016 – 23 percent of which didn’t vote for Clinton, either by abstaining or picking another candidate. Here are the false stories, along with the percentages of Obama supporters who believed they were at least “probably” true (in parenthesis):

– Clinton was in “very poor health due to a serious illness” (12 percent)

– Pope Francis endorsed Trump (8 percent)

– Clinton approved weapons sales to Islamic jihadists, “including ISIS” (20 percent)

Overall, about one-quarter of 2012 Obama voters believed at least one of these stories (26 percent). And of that group, just 45 percent voted for Clinton – compared to 89 percent who believed none of the three.

This alone does not prove that fake news was a difference-maker, of course. A recent Princeton-led study of fake news consumption during the 2016 campaign found that fake news articles made up only 2.6 percent of all hard-news articles late in the 2016 election, with the stories most often reaching intense partisans who were likely not persuadable. And it wouldn’t be surprising if Obama voters who weren’t reliable Democratic supporters were more apt to believe fake news stories that affirmed their decision not to vote for Clinton.

So the researchers sought to control for other factors like gender, race, age, education, political leaning and even personal feelings about Clinton and Trump using multiple regression analysis. According to the researchers, all of these factors combined to explain 38 percent of the defection of Obama voters from Clinton, but belief in fake news explained another 11 percent.

For those defecting from Clinton, believing fake news had a greater impact than anything except being a Republican or personally disliking Clinton. Obama voters who believed one of these fake news stories “were 3.9 times more likely to defect from the Democratic ticket in 2016 than those who believed none of these false claims, after taking into account all of these other factors,” the researchers write.

“We cannot prove that belief in fake news caused these former Obama voters to defect from the Democratic candidate in 2016,” they write. “These data strongly suggest, however, that exposure to fake news did have a significant impact on voting decisions.”

Exactly how that translates into raw votes and whether it swung the election is the big, unanswered question – and the one that seems to preoccupy Trump. It’s difficult to know how fake news played specifically in the three states that delivered him the presidency: Michigan, Pennsylvania and Wisconsin. But the fact that Clinton lost each of these divisive states by less than one percentage point means that even a slight impact by Russia and/or fake news – or even then-FBI Director James Comey’s announcement about Clinton’s emails or some other factor – could logically have changed the result.

But we can use this study to glean some clues and even rerun a hypothetical 2016 election. The Washington Post’s polling director, Scott Clement, ran a predictive probability analysis using the OSU team’s data and compared the existing 2016 election to a hypothetical election in which these fake news stories didn’t exist. The result: Clinton lost 4.2 percent more of Obama’s votes in the race with fake news, versus the hypothetical race without it. The study notes that 10 percent of Obama voters voted from Trump.

If we multiply that 4.2 percent drop-off by Obama’s 2012 vote share in the three key states that delivered the presidency to Trump, it suggests fake news cost Clinton around 2.2 or 2.3 points apiece in Michigan, Wisconsin and Pennsylvania. And Clinton lost Michigan by just 0.2 points and Pennsylvania and Wisconsin by 0.72 and 0.76 points, respectively.

These are rough estimates, to be clear. But notably, Clinton’s estimated drop-off in each state would be about three times bigger – or more – than the study’s impact of fake news. That would mean that, for fake news not to have made the difference (according to these data), Michigan, Pennsylvania and Wisconsin would have had to be uniquely impervious to the effects of fake news, when compared to the rest of the country.

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Some Democrats – but not Biden – talk of expanding SCOTUS The survey also notably doesn’t measure what impact fake news might have had in increasing Trump’s support, instead only focusing on how it depressed Clinton’s. That could actually increase the shift. But even with this limited purview, it suggests it made a significant difference.

And it suggests it may well have cost Clinton the presidency.

The Washington Post’s Scott Clement contributed to this report.