In Social Media and Fake News in the 2016 Election, Hunt Allcott (NYU) and Matthew Gentzkow (Stanford) conclude “our data suggest that social media were not the most important source of election news, and even the most widely circulated fake news stories were seen by only a small fraction of Americans. For fake news to have changed the outcome of the election, a single fake news story would need to have convinced about 0.7 percent of Clinton voters and non-voters who saw it to shift their votes to Trump, a persuasion rate equivalent to seeing 36 television campaign ads.”
Here’s the abstract to their NBER report:
We present new evidence on the role of false stories circulated on social media prior to the 2016 US presidential election. Drawing on audience data, archives of fact-checking websites, and results from a new online survey, we find: (i) social media was an important but not dominant source of news in the run-up to the election, with 14 percent of Americans calling social media their “most important” source of election news; (ii) of the known false news stories that appeared in the three months before the election, those favoring Trump were shared a total of 30 million times on Facebook, while those favoring Clinton were shared eight million times; (iii) the average American saw and remembered 0.92 pro-Trump fake news stories and 0.23 pro-Clinton fake news stories, with just over half of those who recalled seeing fake news stories believing them; (iv) for fake news to have changed the outcome of the election, a single fake article would need to have had the same persuasive effect as 36 television campaign ads.