Donald J. Trump routinely raises the issue of crime on the campaign trail, saying that it is “through the roof” and that cities like Philadelphia are “ravaged by bloodshed.”

Philadelphia, like many other American cities, endured a sharp spike in homicides during the pandemic. But now many of those same places are seeing a sharp drop, including in swing states. In Arizona, the decline in violent crime is even steeper than the national average.

But falling crime does not necessarily translate into voter comfort, said Paul Sracic, a political science professor at Youngstown State University in Ohio.

“When we talk about crime, in some ways it’s similar to how we talk about economics in that perception matters,” Dr. Sracic said, adding, “Perception is as important as reality — and maybe more important than reality to voters.”

Republicans have tried to tie crime to immigration, with ad after ad connecting the wave of migrants at the border with fentanyl overdoses, murder and rape. (Research shows that immigrants commit crime at a much lower rate than native-born Americans do.)

Democrats are talking more about crime as well, said Insha Rahman, the director of Vera Action, which works to reduce incarceration. While Republicans still spend more on campaign ads about crime, they no longer spend three or four times more, she said.