“In the political space, you no longer have to have facts to back up your claims,” said Talia Stroud, director of the Center for Media Engagement at the University of Texas. “The result is a population bordering on cynicism, where people discount everything that’s opposed to their views.”

The loss of shared facts can be corrosive for rational discourse, as in Russia, where political leaders learned to use the online explosion far ahead of the United States.

“They spread this sense that people live in a world of endless conspiracy, and the truth is unknowable, and all that’s left in this confusing world is me,” said Peter Pomerantsev, author of “This is Not Propaganda: Adventures in the War Against Reality.” He was referring to Russian President Vladimir Putin and other authoritarian rulers. Mr. Trump, he said, has that style too.

Mr. Pomerantsev, who worked in a Russian television station in the early 2000s, said there is a transgressive thrill in strong leaders thumbing their nose at the facts.

“We slightly miss the point if we don’t understand how much pleasure their supporters derive from this,” he said. “Did he really say that? You can’t stop watching him. It’s partly about power. But it’s also anarchic, and there’s a weird freedom in that.”

Mr. Trump’s approach does not appeal to everyone, though, even in his own party.

“I do not support this brand of politics — any time there is any type of controversy, you just flatly deny it and you do it over and over until people are exhausted and move on,” said Mr. Memory, the computer programmer. Mr. Memory, a registered Republican, said that was why he did not vote for Mr. Trump.

But he said he sees bias among liberal news outlets and that drives him crazy too. He was annoyed, for example, that stories of Mr. Trump being booed at the Washington Nationals baseball game were given top billing, but when Mr. Trump was cheered in Alabama a few days later, he could find almost nothing about it.