As a result, a 2012 Fairleigh Dickinson University poll found that 37 percent of Democrats think it is “probably true” that “President Bush’s supporters committed significant voter fraud in order to win Ohio in 2004,” and 36 percent of Republicans endorsed the claim that “President Obama’s supporters committed significant voter fraud in the 2012 presidential election.”

Most recently, supporters of Bernie Sanders spread similar conspiracy theories that Hillary Clinton’s campaign used election fraud to win the Democratic nomination.

Though these misperceptions are bipartisan, Republicans are especially vulnerable because they are already so distrustful of the voting system. Mr. Sances and Mr. Stewart found that the percentage of Republicans who are very confident in the national vote declined by 40 percentage points between 2000 and 2012. This decline was sharpest during the Obama years and would probably continue if the G.O.P. lost a third consecutive presidential race. They may also be suspicious of another Democratic victory because of the long-term campaign to promote the myth of widespread voter fraud, which has prepared Republicans to believe in a claim of a stolen election.

Despite the public’s tendencies to blame a loss on fraud, no losing presidential candidate has ever endorsed such a claim. The results of a 2002 academic experiment involving a challenge by a losing candidate suggest that the consequences of a candidate endorsement would be substantial. This effect could be intensified by favorable coverage of voter fraud claims in allied media outlets, where Mr. Trump’s claims are already being amplified by supporters. Research in Europe shows that high news consumption in polarized media environments widens the gap in the perceived legitimacy of the political system between supporters of winning and losing candidates.

Even if he contests a loss, Mr. Trump will not undermine American democracy by himself. The institutions and norms of the system are strong enough to withstand such a challenge. But questioning the integrity of the electoral system could encourage other losing candidates to challenge their own defeats, creating the risk of a more serious crisis of legitimacy in the future.