F. Scott Fitzgerald famously declared that “the test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” Compassion and strong leadership are not even opposed — yet these days, they can’t seem to be held in the same political mind. What a sad commentary on our times.

But in this dreary stalemate lies a tremendous opportunity. Mr. Hayes’s research shows that Americans love a leader who throws out the usual script and trespasses on traits that traditionally belong to the other side. Combing through decades of data, he finds that on average, if voters rate two candidates as equally strong leaders (meaning the Democrat has erased his party’s usual deficit on this trait), they break roughly 60 percent to 40 percent in favor of the Democrats. Conversely, among voters who rate a Republican candidate and a Democratic one as equally empathetic, the G.O.P. wins with about 65 percent. Voters reward candidates who go after unconventional traits.

This brings us to the high-profile anti-poverty initiatives from trait-trespassing Republicans such as Senator Marco Rubio and Representative Paul D. Ryan. Mr. Ryan’s new anti-poverty plan, for example, features an expansion of the earned-income tax credit for childless workers — an outstanding idea that Democrats have favored for decades. The Washington Post declared the plan “so bipartisan it doesn’t sound like he’s running in 2016,” supposing that Mr. Ryan’s proposal might even jeopardize his chances with the Republican base.