Supporters hold signs as they wait for Republican presidential nominee Donald Trump to speak during a campaign event Wednesday in Orlando (Jabin Botsford/The Washington Post)

Elections are word problems. If a Trump Train leaves Grand Central Terminal on June 16, picking up white men without college degrees at every stop and letting off white women with college degrees, will it get to Washington before or after Hillary Clinton's Scooby Doo van — loaded with Hispanic voters and women but fewer African Americans than expected — that left from Chappaqua two months earlier?

That's a joke, but the core is accurate. What will the composition of each candidate's supporters look like? And, more important, how many will actually come out to vote?

Since The Washington Post and our partners at ABC News started tracking the presidential race, Trump quickly closed a gap between himself and his opponent, with Clinton now retaking a slight lead. A lot of this is driven by enthusiasm, our pollsters note, but the closer race was also a function of Republicans coming back home to Trump.

In part, it seems, that's the result of a movement among college-educated white men. Looking at three days of polling — Oct. 27, when Clinton's lead was largest; Tuesday, when Trump led; and Thursday — you can see that the margin of support Trump has among Republicans increased by about eight points since a few weeks ago. (He also gained three points from Democrats and two from independents, but that's probably statistical noise.) There's a correlation between poll results and how much support Trump gets from his own party vs. how much Clinton gets from hers. A more solid base means more solid results for Trump.


Notice, too, the big swings among white men with college degrees. The margins of error here are larger than among the parties, but Trump went from trailing Clinton by six points to leading her by 11 on Tuesday, settling back down a bit to lead her by four now.

The picture this paints? Whites with college degrees have consistently preferred the Republican to the Democrat in presidential races, according to exit polling. For most of this year, that hasn't been the case. The Post's James Hohmann called white college-educated women Clinton's “firewall” in polling, which is probably true. But white college-educated men seem to be a swing group here.

That overlaps with another interesting finding, from a poll conducted by Morning Consult and Politico.

We've talked before about the Trump campaign's complaint — issued mostly when he's trailing — that there's a hidden vote out there that pollsters aren't capturing. It has never been articulated who those voters are, but the idea stems from the idea that social pressure might make people reluctant to tell a pollster who asks about an election whom they actually support. (This is commonly called the “Bradley effect,” referring to a black California gubernatorial candidate in 1982 who was leading in the polls but eventually lost. The operating theory was that voters wanted to seem more receptive to a black governor than they actually were.)

The Consult-Politico pollsters figured out a nifty way to test this. They conducted identical online and phone surveys, operating under the idea that the “social pressure” effect would be lower when there wasn't a real person to speak to. We looked at this idea on Monday, comparing public polls conducted using live callers with online polls. The Consult-Politico poll, though, controls for a lot of other factors that comparing polls from different outlets couldn't.

What did they find? That overall, there wasn't much of an effect. Among those with college degrees, though, there was a small effect (once you consider margin of error).


(There was also an effect in which higher-income respondents showed a similar shift, but income often correlates to education.)

We asked Morning Consult what the gender split among college-educated respondents was. There was a similar effect among both men and women, but only among men did Trump lead in online polls. If college-educated women are slightly more supportive of Trump than other polls suggest, though, that's a small crack in Clinton's firewall.


The overall effect of the “shy Trump vote” wasn't going to be enough to swing the election, Morning Consult wrote, given that the effect they found was small and only among a portion of the electorate.

It's worth wondering why the effect exists, though. The data are vague, but one possible story is this: Our tracking poll suggests that Republicans (and the white men with college degrees in that group) were iffy on Trump. They climbed on board recently. The Morning Consult-Politico poll may have captured that wavering: talking to a real person, college-educated voters said “Clinton,” but some were really leaning to Trump or still undecided. That poll was in the field as our polls showed a tightening race (from Oct. 27 to 30) -- maybe the results now would be different.

It's hard to say. As Nate Cohn of the New York Times points out, there's no evidence that the “hidden vote” is among Trump's core base of support, non-college-educated white men. (This will surprise no one who has experienced the fervor that Trump's base exhibits.) A majority of that group is on the Trump Train, as they have been from the outset. It's college-educated people who seem to be most reluctant to admit buying a ticket on the train — and who are making this particular word problem somewhat tricky to answer.