There is no way to quantify exactly what this barrage of disinformation and manipulation did to American politics. But it should be obvious that what happens online influences our perceptions of, and behavior in, the offline world.

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This year, researchers at Ohio State University tried to measure the impact that fake news had on the 2016 election. They based their analysis on a postelection survey in which they’d asked voters 281 questions, three of which were intended to determine their exposure to online disinformation.

Respondents were asked to rate the accuracy of statements claiming that Hillary Clinton was suffering from a serious illness, that she’d approved weapons sales to the Islamic State group as secretary of state, and that President Donald Trump had been endorsed by Pope Francis. “Belief in these fake news stories is very strongly linked to defection from the Democratic ticket by 2012 Obama voters,” wrote the researchers, Richard Gunther, Paul A. Beck and Erik C. Nisbet. Even after controlling for variables like ideology, education, party identification and dislike of Clinton, they found that believing a fake news story made people who voted for President Barack Obama in 2012 significantly less likely to vote for Clinton in 2016.

The study’s authors don’t claim a clear causal link between propaganda and voting; it’s possible that people who rejected Clinton were more open to misinformation about her. It’s hard to believe, however, that at least some of them weren’t affected by a social-media ecosystem saturated with deliberate lies.

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Still, many people on both the left and the right have been skeptical of the notion that Russia’s industrial-scale trolling campaign made a significant difference in Trump’s election. In February, special counsel Robert Mueller indicted 13 Russians connected to the internet Research Agency, a Russian trolling operation based in St. Petersburg. Shortly afterward, National Review’s Rich Lowry scoffed that the “Russian contribution on social media was piddling and often laughable.”

That month, Adrian Chen, who reported on the internet Research Agency for The New York Times Magazine, appeared to minimize its political impact in an interview on MSNBC. He called it “essentially a social media marketing campaign with 90 people, a few million dollars behind it, run by people who have a bare grasp of the English language and not a full understanding of who they’re targeting.”

At a conference in Germany in July, I met Denis Korotkov, a brave Russian journalist who has reported extensively on Yevgeny Prigozhin, the oligarch behind the troll factory, who was included in Mueller’s February indictments. Speaking through an interpreter, he expressed incredulity at the idea that the misinformation being spread from St. Petersburg could have changed the direction of American history.

But it looks increasingly as if it did. On Monday, the Senate Intelligence Committee released two reports it commissioned about the nature and scale of Russia’s social media disinformation campaign. One was produced by New Knowledge, a Texas cybersecurity company, along with researchers at Columbia University and Canfield Research; the other was written by researchers at Oxford University’s Computational Propaganda Project along with Graphika, a company that analyzes social media. They were based on (incomplete) data turned over to Congress by several major social-media platforms, and they suggest the campaign was more extensive and sophisticated than has been previously understood.

Russian propaganda, one of the reports found, had about 187 million engagements on Instagram, reaching at least 20 million users, and 76.5 million engagements on Facebook, reaching 126 million people. Approximately 1.4 million people, the report said, engaged with tweets associated with the internet Research Agency. “The organic Facebook posts reveal a nuanced and deep knowledge of American culture, media and influencers in each community the IRA targeted,” it said.

There is no way to quantify exactly what this barrage of disinformation and manipulation did to American politics. But it should be obvious that what happens online influences our perceptions of, and behavior in, the offline world. People have committed horrific acts of violence based on Facebook propaganda. The Islamic State group has used Twitter to recruit alienated Westerners.

Looking at Israel’s airstrikes on Gaza in 2012, Thomas Zeitzoff, an associate professor at American University, found that they’d significantly slow when there was a sharp uptick of online support for Hamas, an indication that the Israeli Defense Forces were monitoring their reputation on social media. Influencer marketing wouldn’t be a billion-dollar industry if corporations didn’t think social media shapes behavior.

In October 2016, Libby Chamberlain founded an invitation-only Facebook group called Pantsuit Nation as a safe space for supporters of Hillary Clinton. The fact that people felt like such a space was necessary is testament to how intimidated a great many Clinton supporters were by the vicious climate online. “As much as possible,” Chamberlain told The Washington Post, her group “removes the risk that they’re going to be attacked for their views.”

Some of these attacks came from real people, but not all. In their book “LikeWar: The Weaponization of Social Media” — which is where I learned about Zeitzoff’s study — P.W. Singer and Emerson T. Brooking described how, in the run-up to the election, “anti-Clinton botnets actively sought out and ‘colonized’ pro-Clinton hashtags, flooding them with virulent political attacks.” These attacks helped make fervent Clinton supporters reluctant to go public online. That, in turn, created a widespread impression that Clinton lacked enthusiastic grass-roots support, which is belied by the fact that Pantsuit Nation quickly swelled to millions of members.

In an election decided by a rounding error — fewer than 80,000 voters spread over three states — Russian trolling easily could have made the difference. It’s mortifying and preposterous that fake news ruined America. That doesn’t mean it isn’t true.