The North Carolina man who took an assault rifle to a popular D.C. pizza joint to investigate a fictitious online rumor demonstrates a problem that has long vexed the FBI.

The Internet — a breeding ground for radical ideologies and bizarre conspiracy theories — can quickly move troubled souls to violence. And in an age when fake news is magnified by those with political and financial interests, the problem is getting harder to stop.

The bureau has in recent years made a priority of preventing Islamic State-inspired attacks, developing informants who can tip agents to plots before they happen and connecting the often Internet-radicalized plotters with people actually working for the FBI.

But the bizarre conspiracy theory that a child sex ring was operating underneath D.C.’s Comet Ping Pong restaurant — which spurred 28-year-old Edgar Maddison Welch to drive from North Carolina to launch his own violent investigation — would probably have registered as “barely a blip” on the bureau’s radar, said Ron Hosko, a former FBI assistant director.

[Pizzagate: From rumor, to hashtag, to gunfire in D.C.]

Comet Ping Pong customers came out to support the restaurant after a gunman entered it with an assault rifle, firing it at least once. Several other businesses on the block have received other threats as well. (Whitney Shefte/The Washington Post)

“There is so much to do that is tangible and real and fitting squarely within the bureau’s jurisdiction and priorities,” Hosko said. “There’s not a lot of bandwidth for sort of these one-offs.”

That is not to say online radicalization, in all its forms, is not a concern for federal law enforcement. Research has shown people who believe in conspiracy theories are more prone to violence. On Wednesday, for example, federal authorities in Florida announced they had indicted a Florida woman who they alleged threatened the parent of a child killed in the massacre at Sandy Hook Elementary School in Newtown, Conn.

The woman, 57-year-old Lucy Richards, was motivated to make her threats because she believed, incorrectly, “that the school shooting was a hoax and never happened,” according to the U.S. Attorney’s Office for the Southern District of Florida.

At an event earlier this year to mark the 10th anniversary of the Justice Department’s National Security Division, FBI Director James B. Comey said agents were focused on a “much more disparate threat” that was “hard to see, unpredictable, motivated, and driven by people who are just disturbed and unpredictable even to those who would motivate them.”

“Our daily job is finding needles in a haystack,” he said. “As I like to say, it’s harder than that even. It’s finding pieces of hay that may become a needle.”

The FBI declined to make an official available for an interview for this article.

The false theory that spurred Welch to action — that a child sex ring tied to Democratic presidential nominee Hillary Clinton and campaign chairman John Podesta was operating beneath Comet Ping Pong — spread through Twitter, 4chan and Reddit, and was magnified on Infowars by talk-show host Alex Jones. People came to refer to it by the hashtag “Pizzagate.”

The FBI and D.C. police assessed the claims and determined them to be false, according to a D.C. police spokesman and a federal law enforcement official. But the rumor nonetheless prompted threats and harassment of the shop and neighboring businesses on Connecticut Avenue, and some business owners said they were frustrated by law enforcement’s response. A D.C. police spokesman said he was unaware of any threats Welch made himself.

There are several well-known examples of conspiracy theorists carrying out acts of violence. Robert Dear, who allegedly killed three people and wounded nine others in an attack on a Planned Parenthood facility in Colorado, told a neighbor that he believed the government was “trying to kill everybody.” A Twitter account linked to one of the Boston Marathon bombers seemed to espouse the view that the terrorist attack of Sept. 11, 2001, was an “inside job.” In a more recent case, the FBI arrested a Milwaukee man, Samy Mohamed Hamzeh, who the agency alleged was plotting a mass shooting at a Masonic temple and believed Masons were “playing with the world like a game.”

Joseph Uscinski, an associate professor at the University of Miami and a co-author of “American Conspiracy Theories,” said research has shown “people who have a very conspiratorial mind-set tend to be more accepting of violence than people who don’t have a conspiratorial mind-set, but it’s not by much.”

Fake news and conspiracy theories have other pernicious effects. The Russian government, for example, reportedly tried to spread false materials online to affect the election. At the National Security Division event earlier this year, Comey said he was concerned that Twitter in particular allowed people to reinforce their own views, irrespective of facts, and that this eroded trust in government institutions.

[People who believe in conspiracy theories are more likely to endorse violence]

“It used to be that the person who’s now on Twitter would be down at the end of the bar late at night shouting at the television, and the only people he could shout with would be the other people who were down at the end of the bar,” Comey said. “Now he can shout with 600 other people who are at their own metaphorical bars, and it’s a constant reinforcement of their view of the world.”

The First Amendment prevents law enforcement agencies from policing free speech. Cass Sunstein, a Harvard professor and former White House official, proposed controversially in 2008 that the government engage in “cognitive infiltration of extremist groups,” by enlisting government agents to enter chat rooms and raise doubts about conspiracy theorists’ ideas. In one variant, he wrote, “government officials would participate anonymously or even with false identities.”

The proposal was criticized by those on the right and the left, and even Sunstein and his co-author acknowledged that it came with the risk that the government might inadvertently legitimize bad information. Sunstein declined to be interviewed for this article.

Justice Department guidelines say that agents can surf the Internet in search of possible terror plots, though a former federal national security official said agents have little time to randomly browse the Web to generate leads. Generally, the former official said, the FBI foils plots because would-be plotters reveal their intentions to the bureau’s informant network, or from concrete tips they run down.

“You can’t monitor 330 million Twitter [users] and their traffic, nor would you want to do that,” the former official said, speaking on the condition of anonymity to discuss FBI methods. “That’s the beauty of living in a free society. You’re allowed to be crazy.”

Law enforcement has occasionally drawn criticism for taking an overly aggressive approach — particularly with surveillance of the Muslim community. The New York Police Department, for example, was sued over its surveillance of Muslims in a case in which settlement discussions are ongoing. The FBI was accused of going too far in using an informant to infiltrate a mosque in California.

Some Islamic State-inspired terrorists have slipped through the cracks — such as Omar Mateen, the 29-year-old who killed 49 people in an Orlando nightclub. The FBI had scrutinized Mateen for 10 months beginning in 2013, even using surveillance and recording his calls after he talked of dying as a martyr, though they ultimately closed the matter without charges.

The threshold to take action on even a threat, Hosko said, is fairly high. The matter is generally left to local authorities unless the threat comes from across state lines, and incendiary rhetoric usually cannot be investigated. Given the volume of such cases, Hosko said, agents generally assess even in real threat cases whether the person was willing and able to follow through.

“The question for the FBI is, ‘Is there a case we can prosecute?’ ” Hosko said. “Is this serious enough? Do we devote the resources?”

Uscinski, the University of Miami professor, said conspiracy theories are generally directed at those in power, and he expected more in the coming years would come from the left, rather than the right. But Trump, he said, has in some ways flipped the normal logic, raising conspiracy theories about the powerless — such as Mexico sending its rapists over the border — that could lead to attacks on those with little ability to stop them.

“To see those sorts of conspiracy theories sort of worries me,” Uscinski said, “because if Trump doesn’t act, you could see someone sort of act on his behalf, against people who are unprotected.”

Adam Entous and Mark Berman contributed to this report.

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