“There’s a great human capacity for inventing things that aren’t true about elections,” said Frank LaRose, a Republican who serves as Ohio’s secretary of state. “The conspiracy theories and rumors and all those things run rampant. For some reason, elections breed that type of mythology.”

Steve Simon, a Democrat who is Minnesota’s secretary of state, said: “I don’t know of a single case where someone argued that a vote counted when it shouldn’t have or didn’t count when it should. There was no fraud.”…

The New York Times contacted the offices of the top election officials in every state on Monday and Tuesday to ask whether they suspected or had evidence of illegal voting. Officials in 45 states responded directly to The Times. For four of the remaining states, The Times spoke to other statewide officials or found public comments from secretaries of state; none reported any major voting issues.

Statewide officials in Texas did not respond to repeated inquiries. But a spokeswoman for the top elections official in Harris County, the largest county in Texas with a population greater than many states, said that there were only a few minor issues and that “we had a very seamless election.” On Tuesday, the Republican lieutenant governor in Texas, Dan Patrick, announced a $1 million fund to reward reports of voter fraud.