What’s the best estimate? That’s a matter for debate.

“The truth, if you could ever get to it, is probably somewhere between the three measures,” said Joe Lenski, the vice president at Edison Research, who runs the exit poll, “because they all have their faults.”

They do have their faults. Just about every year, the census reports more people voted than actually did — especially in Southern states with a large black population. The census also has a challenge with people who decline to say whether they voted.

Things can go wrong with the voter file, too, if, say, the state erred in data entry or updates. The models are imperfect as well.

But for many experts in the field, these issues pale next to those facing the exit polls. For Bernard Fraga, a professor of political science at Indiana University, there is “no question that the exit poll is not as accurate.” He added, “It’s clearly much more reliable to look at the C.P.S. or even better to look at the voter file-based work.” Today, virtually all major campaign polling, voter targeting and election law litigation is conducted using voter file data.

The actual results also tend to imply that the census and Catalist figures make a lot more sense in many of the cases where the disagreements are greatest.

Take Ohio, where the exit polls show that the black share of the electorate increased by four percentage points to more than 15 percent of voters in 2012. If these figures are taken as precise, it would imply that nearly 250,000 more black voters turned out than in 2008, with the turnout reaching 88 percent of adult black citizens. There is no trace of this kind of surge in turnout in the actual result. The black turnout in Cleveland actually dropped — to 55 percent of adult citizens.

This type of story repeats itself across the battlegrounds. It also plays out with age, where the exit polls imply that youth turnout was higher than turnout among seniors; with education, where the exit polls show that more college graduates voted than actually live in America; or Hispanics, where the exit polls show that white and Hispanic turnout was nearly equal, despite decades of evidence to the contrary. You can see more of this data here.

The Democratic Dependence on White Working-Class Voters

The larger number of white working-class voters implies that Democrats are far more dependent on winning white working-class voters, and therefore more vulnerable to a populist candidate like Mr. Trump.

Over all, 34 percent of Mr. Obama’s supporters were white voters without a college degree, compared with 25 percent in the exit polls, according to an Upshot statistical model that integrated census data, actual results and 15,000 interviews from various pre-election surveys. The model yields a full alternative to the exit polls that assume an older, whiter electorate like the one depicted by the census. (For those interested in the details about our estimates, we’ve written a technical sidebar.)

“This is a great way to deal with the limits of traditional surveys,” said Andrew Gelman, a professor at Columbia who popularized the statistical technique known as multilevel regression and post-stratification. “It smooths out noise, reduces bias and arrives at better estimates for smaller groups.”

Mr. Obama’s dependence among white voters might seem surprising in light of the 2012 postelection consensus. But it won’t be surprising if you think just a little further back — to the pre-election story line. Mr. Obama’s advantage heading into the election was thought to be a “Midwestern Firewall” — a big edge in Midwestern battlegrounds where white working-class voters supported the auto bailout and were skeptical of Mr. Romney, who was criticized for his time at Bain Capital.

The pre-election story line was tossed aside when the national exit polls showed an electorate that was even more diverse than it was in 2008, while showing Mr. Obama faring worse among white voters than any Democrat since Walter Mondale in 1984.

But the Upshot analysis shows that all of Mr. Obama’s weaknesses were in the South — defined as the former Confederacy plus Oklahoma, Missouri, Kentucky and West Virginia — where he won just 26 percent.