Americans are almost evenly divided on whether fraud or voter repression is a bigger problem, despite many studies showing that fraud is almost nonexistent nationwide.

The findings suggest there may be at least some audience for Donald J. Trump’s claims that the presidential election could be “rigged.”

And they dovetail with recent trends. In a Gallup survey in August, 36 percent of Americans said that voter fraud would most likely be a major problem this election, more than those who said it would not be an issue. That was up significantly from a pre-election Gallup poll in 2004, when just 24 percent expressed serious concern about fraud.

“Most pernicious, I think, is the fact that Americans are basically divided on which is the bigger problem, voter fraud or disenfranchisement,” said Robert P. Jones, the chief executive of P.R.R.I.