Volumes have been written in the media about the effect of fake news on the outcome of the 2016 presidential election. Facebook has been pressured to crack down on fake stories in the U.S. and other countries where important elections are taking place this year. It’s rolling out its cooperation scheme with fact-checkers in Germany in the coming weeks. Google has taken steps to discourage spurious news sites. And President Donald Trump himself has adopted the catchphrase “fake news” for his anti-media screeds on Twitter and at his news conferences.

But there have been no serious attempts to quantify the actual influence of fake news stories on how people voted last November until Hunt Allcott of New York University and Matthew Gentzkow of Stanford published a fresh paper. The campaign against them was based on a conclusion based on some truths:

- Sixty-two percent of U.S. adults get news on social networks.

- Fake stories get shared more widely than factual ones.

- People often believe them.

- Most fake stories were pro-Trump.

But does that necessarily mean the fakes increased Trump’s share of the vote?

Allcott and Gentzkow assembled a database of stories deemed fake by fact-checkers, recorded how many times they had been shared on social media (a service called BuzzSumo can be used to extract the data), and asked 1,200 Americans whether they had seen the stories, or at least the headlines (each was shown a random selection of 15 headlines, not the whole database). They even invented fake fake-news headlines as a placebo to keep their respondents honest.

The researchers found out that pro-Trump fake stories had been shared about 30 million times, compared with 7.6 million times for pro-Hillary Clinton ones. About 15 percent of respondents recalled seeing the average fake news headline, and 8 percent recalled believing it when they saw it. Interestingly, the most-remembered fake story was a pro-Clinton one, saying Wikileaks had fabricated compromising emails from leading Democrats.

The numbers, however, were close for the placebo headlines, suggesting people were overstating their exposure.

Correcting for that, Allcott and Gentzkow estimated that only 1.2 percent of people actually recalled seeing the average fake story, meaning the average American remembered about 0.92 pro-Trump fake stories and 0.23 pro-Clinton ones. Not only did the average American remember no more than one fake story, but even smaller fractions of them actually believed it. To sway a voter under these circumstances, the academics estimate that the story would need to be as persuasive as 36 campaign ads.

I have argued that TV ads haven’t been effective in the 2016 campaign. It’s not hard to imagine that one striking story would be more persuasive than a whole bunch of ads. But Allcott and Gentzkow’s conclusion is that the fakes weren’t particularly useful. One reason is that, according to their findings, TV is still a far more important news source for Americans than social media: Only 14 percent of respondents, the fifth biggest share, named the social networks as their number one news source.

The Trump administration threatens to take its message directly to the American people if the media doesn’t give the new president a fair shake. Such unfiltered communication has the advantage of letting Trump say anything he wants, and if fact-checkers have a problem with it, they’re stuck in the unenviable position of running after a train that’s already left the station.

But the results obtained by Allcott and Gentzkow show that most of the U.S. public still won’t receive the unmediated messages. They will hear about Trump tweets and any other direct communication on TV, with whatever spin added by their favorite station, and in most cases, with fact-checks attached. Hype about the omnipotence of social media shouldn’t fool politicians — or anyone, for that matter — about their ability to bypass traditional media. That may be changing — younger people’s consumption habits are different. But will news consumption habits change enough by the next electoral cycle to threaten television’s supremacy? TV-watching dinosaurs are easy to ignore in this age of social media, but they remain all-important to winning presidential elections.

For us in the media business, it’s easy to overestimate how much technology has changed the world. After all, we create the hype around new trends — why shouldn’t we believe it? And yet the underlying mechanics of age-old traditions like electoral democracy do not change as quickly as we might think. That should tell us something important. Instead of panicking about a “post-truth” world, we should raise the bar for our own reporting and make it as persuasive and as fact-rich as we can. Allcott and Gentzkow showed that the brands and reach of traditional media are still strong — but that there is a sizable gap between the number of people who see a major news outlet’s headline and those who believe it as a starting point. That gap is our fault.

Leonid Bershidsky is a Bloomberg View columnist.