The main argument by Mr. Trump and other Republicans is threefold: Voting by mail is easier than going to the polls; more people will vote if the process is easier; and when larger numbers of people vote, more will vote for Democrats.

But in the states and counties that have transitioned to all-mail voting, there has been little evidence of partisan advantage for either side because of mail voting, said Robert Stein, a Rice University professor who has helped put in place vote-by-mail systems.

Amelia Showalter, who was the data analytics director for President Barack Obama’s 2012 campaign, found in deeply reported studies of all-mail elections in Colorado in 2014 and Utah in 2016 that there were very slight partisan advantages in each race.

The Colorado study found that Republicans outperformed their predicted turnout in 2014 by a slightly higher margin than did Democrats. The G.O.P.’s candidate for Senate, Cory Gardner, ousted the Democratic incumbent, Senator Mark Udall, and Republicans won three of the four other statewide races on the ballot.

Two years later, in Utah, Democrats gained an equally slight advantage in counties that had switched to all-mail voting.