“In modern American political history, we’ve never had a major-party presidential nominee allege that the election was stolen from them, let alone an incumbent who has to leave office,” Nyhan said. “The conversation has focused too much on the ‘Will Trump step down?’ question. I’m much more worried about the damage to institutional legitimacy that he can do on the way out.”

Perhaps the most alarming finding of the study is how little effect fact-checking has on the claims. If people believe spurious allegations from Trump and others, and the damage can’t be mitigated by fact-checks, it’s difficult to see how confidence in elections—and by extension, democracy itself—can be rebuilt. The best hope might be to counteract the claims before they take root.

“One of the most effective approaches to countering voter-fraud allegations is to discourage people from making them at all,” Nyhan said. “If media coverage is negative enough, or the political costs are high enough, we know politicians will often avoid making controversial claims.”