The authors ran a series of simulations for elections between 2020 and 2036, using different assumptions about the shape of the electorate, while also trying to estimate how tweaks or shifts in levels of support for Republican or Democratic candidates would affect the popular vote in the states and, therefore, the electoral college and the national totals.

One conclusion is that the country should be braced for repeats of what has happened twice in the past five presidential campaigns — a popular-vote outcome different from the electoral college result. “This report finds quite a few future scenarios could mimic the result of the 2016 election — a Democratic in the popular vote with a Republican win in the electoral college,” the authors write. (The same thing happened in 2000.)

The authors suggest that three demographic changes will have the most significant impact on future presidential elections. The first is the country’s continuing diversification, which means a decline in the percentage of white voters in the electorate and a rise in the percentage of nonwhite voters. Whites constituted 69 percent of eligible voters in 2016, and projections indicate that will decline to 67 percent in 2020 and 59 percent by 2036.