One common approach is to screen voters based on whether they say they will vote. In theory, this method would have the advantage of capturing higher Democratic intention to vote. But it is not obvious whether this potential advantage is being realized here. A YouGov/CBS News poll, for instance, found that self-reported likely voters leaned heavily to Mr. Moore compared with all registered voters. A Fox News poll found the opposite.

Voters just don’t do a great job of accurately reporting whether they’re going to vote.

There’s a lot of evidence that vote history — whether someone voted in previous elections — is a better predictor than people’s self-reported turnout intention.

But the vote-history approach struggles if there isn’t a comparable past election, or if there’s some other reason to think turnout patterns will be different than in the past. A 2004-based turnout model, for instance, could have underestimated black turnout in 2008 when Barack Obama was on the ticket; a 2012-based model could have overestimated black turnout in 2016.

So far in 2017, these kinds of turnout models have underestimated Democratic turnout. That’s in part because they tend to use the turnout data from the last comparable election. In this case, that’s the 2014 midterm, when Democratic turnout was relatively weak. And more generally, young and Democratic-leaning voters have a less robust track record of voting than older and Republican-leaning voters.

One solution might be to estimate turnout using the 2017 special elections, rather than the 2014 midterm in Alabama. But this would mainly increase the estimated turnout among white, Hispanic and Asian-American Democrats, not black Democrats, since black turnout has been comparatively weak so far this year. Because black voters represent around three-fourths of Alabama Democratic primary voters, such a model wouldn’t end up assuming an especially good turnout for Democrats at all. And a 2017-based turnout model would also miss one of the potentially most important dynamics of the Alabama race: low Republican turnout.

So it’s easy to see the turnout challenge for pollsters. A vote-history-based model might understate Democratic turnout. A poll that relies on self-reported vote intention would seem to have a better shot of picking up Democratic strength, but there wouldn’t necessarily be reason to be very confident in its finding.

In a low-turnout election, slightly different assumptions can yield very different results. SurveyMonkey, for example, found a 12-point gap between a typical poll that included registered voters who said they would probably vote and a poll that limited the likely electorate to those who voted in 2014 (or were ages 18 to 20 now, and thus ineligible to vote in 2014, and said they would vote). Similarly, Monmouth found an eight-point gap between a 2014 electorate and a presidential electorate.