As in 2008, being African-American had the greatest effect on someone's vote. Even if all other variables predicted a Republican voter, being African-American meant you were 78 percent likely to vote for Obama. Being nonheterosexual or Hispanic had the next greatest effect in favor of voting for Obama. A born-again Christian or a weekly churchgoer were more likely to vote Republican.
Toward the middle of the list is the effect of union membership and living with a union member. The effect is not as large as most demographic variables.
But it's not nothing; being a member of a union or living with a union member did make a person more likely to vote Democratic. At least according to the 2012 ANES, the effects of the two different union variables were pretty much identical. And the impact was about the same as the 1.7 percentage points it was in 2008.
In the ANES data set, 58 percent of union members or those living with a union member voted for Obama. If every union member or member of a union household voted as if they were not one and every other characteristic was kept constant, 51.1 percent of them still would have voted Democratic.
Obama would have lost 1.4 percentage points off his vote share in 2012 without unions. Instead of his margin of victory over Romney being 3.9 percentage points, it would have been 1.1 points.
Obviously, this sort of analysis doesn't take into account what would really happen without the union vote. The two parties would go about courting voters differently. And unions also play a big role in fundraising and organizing for Democratic candidates.
But the 2.8 percentage-point difference in the presidential vote margin is nothing to sneeze at either. It's larger than the margin in two of the past four elections, and it's about the same as it was in 2008. Even if unions make up a lower percentage of voters than at any point in the past 60 years, they are a player in presidential elections. And if a future Supreme Court decision suppresses union power further, it would not be good news for Democrats.