DONALD TRUMP often presents himself as the great enemy of fake news. He has a pronounced tendency to accuse his opponents of peddling it. But some suspect it helped to deliver him the White House. One story, widely shared on social media in the run-up to the American election, alleged that the Clinton Foundation bought $137m in illegal arms and organised a child sex ring operating out of a pizza shop in Washington, DC. If this kind of ludicrous story influenced voters and helped push Mr Trump into the presidency, then the implications for American democracy are grim. Speaking truth to power is harder in a world where lies are cooked up for clicks.

A new working paper by two economics professors, Hunt Allcott of New York University and Matthew Gentzkow of Stanford University, is the first major study to have a data-driven crack at this topic. Though they do not estimate the impact of fake news directly, their findings suggest that for it to have been pivotal, each fake article would have had to have an impressively large effect on voters.

The authors collected a database of fake news stories shared before the election and surveyed 1,200 Americans about them. These fake stories seemed very much slanted in favour of Mr Trump. In the three months before the election, Americans shared pro-Trump fake news stories 30m times on Facebook—almost four times more than false news favouring his opponent, Hillary Clinton. It seems that seeing was believing. Half of the people surveyed who viewed a fabricated headline believed it, compared to 10% of those who had not.



Messrs Allcott and Gentzkow compute a sense-check on whether these fake news stories swung the election, by referring to good evidence on the effect of watching a TV campaign ad on vote switching. By assuming that exposure to a campaign commercial increases the probability of a switched vote by a fixed amount, political scientists have come up with reasonable, (more or less causal) estimates for the persuasiveness of an individual ad.

But first, they had to iron out an important wrinkle: Americans’ fickle memories. Respondents to their survey were just as likely to say they had seen a “placebo” collection of fake news stories invented by the authors as ones that had actually been circulated (see chart below). After accounting for this tendency for false recall, which would tend to overstate exposure to fake news, as well as a few other simplifying assumptions, Messrs Allcott and Gentzkow calculated that in order for fake news to have swung the election, the articles would need to be 36 times as persuasive as a televised campaign ad.

Their analysis has something of a sausage factory about it—the outputs are more appealing than the inputs. The lack of difference between recall rates of the “real” fake news and the “fake” fake news is worrying, as it suggests that respondents were guessing for all of their answers. On the other hand, it could reflect the fact that their placebo, “fake” fake headlines were too plausible, in which case their correction would significantly underestimate exposure to fake news. Whichever is true, their main finding, that fake news would need to be overwhelmingly more powerful than television ads to have changed the election result, holds up. False headlines might have contributed to the election outcome, but the evidence here does not suggest that it was pivotal.

All this is not to say that people should not worry about a slow descent into a post-truth world. Although it seems unlikely that fake news had a similar effect on vote-switching to television ads (14% of those surveyed in the study reported that social media was their “most important” news source) the corrosive effects of disinformation on public trust in institutions should not be dismissed. Just as bad, it can reinforce an already polarised political landscape. The economists found that Republicans are 300-700% more likely than Democrats to believe false pro-Trump headlines, while Democrats are 50-100% more likely to lap up pro-Clinton ones.

Facebook, for its part, is changing its policies after a sluggish response to false stories before the election. The company announced this week that fake news articles in Germany will be marked as “disputed” ahead of the country’s elections in the fall. (Recently, a swirl of fake allegations began circulating concerning Angela Merkel, Germany’s chancellor, who was said to be cavorting with terrorists.) Articles based on outright fabrications are just one of the ways in which news can mislead. Yet it might also be the easiest, technologically, to filter out. And every little helps.