It was a time, therefore, when one would expect ex-felons to have been particularly likely to register to vote, either as a result of mobilization efforts or because of the prospect of supporting the first black president.

The ex-felons were indeed overwhelmingly likely to register as Democrats. In North Carolina, they registered as Democrats by 55 percent to 10 percent. The tallies were similar in two other states where the study was conducted: New Mexico, at 52 percent to 19 percent for Democrats, and New York, at 62 to 9.

Yet in the end, just 33 percent of these newly eligible voters registered for the 2008 election in North Carolina, and just 21 percent voted. The registration and turnout rate in New Mexico and New York were far lower, with 13 percent turnout in New Mexico and 8 percent turnout in New York (for 2012; that study counted discharges from 2008 to 2012).

So what does that mean for Virginia? Imagine, for a moment, that the same figures for North Carolina played out in Virginia: 21 percent of the 200,000 re-enfranchised ex-felons turn out, and they vote Democratic by an 85-to-15 margin. The result would expand the Democratic vote margin by 29,400 votes. In the 2012 election, that would have increased Mr. Obama’s margin of victory to 4.6 percentage points from 3.9.

Again, this represents something of a best-case scenario for Democrats. The turnout rate among newly registered ex-felons was high: 69 percent among active registered voters.

The Obama campaign’s effort in North Carolina was aided by the state’s voter file, which includes the race of registered voters. That allowed the Obama campaign to aggressively target newly registered black voters ahead of the election. The campaign of the Democratic nominee won’t have that advantage in Virginia, where race is not listed in the voter registration file. This is not a small matter.