“Fake news” is an all-purpose non-sequitur at this point, but the term does describe a relatively new phenomena popularized in the 2016 presidential election: deliberately fabricated (as opposed to erroneous or biased) stories from little-known sources, which could spread rapidly through direct sharing on sites like Facebook. But did these false stories meaningfully affect how Americans voted? A study by two economists concludes that they probably didn’t — in part because most people seemed to barely remember them.

The paper, written by Stanford University professor Matthew Gentzkow and NYU professor Hunt Allcott, aims to calculate the effect of “fake news” by answering a few basic questions. First of all, how many Americans read and trust news they find through social media? Second, how many remember seeing or believing specific false stories about candidates Donald Trump and Hillary Clinton? And third, how do these results compare to the persuasive power of older media, like television?

To gather data, Gentzkow and Allcott ran an online survey of 1,208 US adults in late November, a few weeks after the election. Alongside questions about demographics and political affiliations, the survey asked participants for their “most important source of news and information” about the 2016 election. Then, it presented them with 15 headlines, equally split between pro-Clinton and pro-Trump news. These were a mix of unambiguously false stories, unambiguously true ones, and placebo headlines — made-up claims that neither real nor fake news outlets had reported. It asked them whether they’d seen each one “reported or discussed” during the campaign, and whether at the time of the election, their “best guess” would have been to believe it.

“People were no more likely to recall seeing actual fake headlines than they were to falsely recall placebo headlines.”

True headlines included Trump refusing to confirm that he would concede the election if he lost, as well as Clinton’s comment about Trump supporters belonging in a “basket of deplorables.” False ones included a claim that the Pope had endorsed Trump, that Trump had groped drag queen RuPaul, and that the FBI found evidence of the Clinton Foundation running a pedophile ring. Placebos included claims that either Trump or Clinton campaign staff had diverted funds to buy alcohol for expensive parties.

About 15 percent of the respondents said they’d seen the average fake news headline, and 8 percent said they’d seen and believed it. (Far more people remembered the true stories.) But a similar number reported seeing and believing placebo stories — in other words, the study’s fake fake news, which they almost certainly hadn’t encountered. “People were no more likely to recall seeing actual fake headlines than they were to falsely recall placebo headlines,” the authors say. Based on this, they calculated a sharply reduced estimate of how much people actually remember false headlines.

Meanwhile, less than 14 percent of respondents said their primary source of election news was social media, while around 15 percent relied primarily on websites. Over 57 percent relied on cable, network, or local TV news, with the remainder split between print and radio.

Taking into account how many times each of the (real) fake headlines had been shared, the authors say the average American would have remembered 0.92 pro-Trump fake stories during the election, and 0.23 pro-Clinton ones. About half the people who remembered seeing a story said they believed it.

Even if “fake news” didn’t sway voters, most of it favored Trump

As this suggests, the authors did encounter far more pro-Trump fake news shares — 30.3 million shares for false stories that favored Trump, versus 7.6 million that favored Clinton. But by extending an existing formula for calculating political persuasion, they concluded that all the fake stories were seen and believed far less than traditional media like television. “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,” the study says. To shift the election, their model suggests that a single fake news story would need the persuasive power of 36 TV campaign ads.

Beyond the general limits of self-reported survey data, many of the numbers here are calculated with assumptions about things like how much fake news is out there, how evenly it’s distributed, and how persuasive people find it. But an earlier survey also found that most people forget fabricated stories, although many of the people who did remember the stories believed them. And a Pew survey published today found that more voters paid attention to television than social media.

Not all “fake news” is equal, and individual conspiracy theories can still have harsh consequences — the fact that most people didn’t notice Pizzagate doesn’t mean the few who take it seriously can’t be dangerous. But as Poynter notes, this supports the idea that while made-up headlines might be unsettling, we don’t know how much they affect the average American.

Fake news wasn't the biggest media problem of 2016