Specifically, 64 percent of union members in the Annenberg data set voted for Barack Obama. By contrast, if these same voters were not members of unions but every other demographic characteristic were held constant, the analysis predicts that 52 percent of them would have voted for Mr. Obama instead. Thus, the marginal impact of being a union member on the likelihood on voting for Mr. Obama was 12 percentage points (64 percent less 52 percent) on average. Because about 10 percent of voters in the study were union members, this boosted Mr. Obama’s overall vote share by 1.2 percentage points.

There was also an effect from voters who were not members of a union themselves, but had someone else in their household who was (these voters are designated as “union member in household” in the chart). These respondents, which represent about 5 percent of the Annenberg data set, were between 8 and 9 percentage points more likely to vote for Mr. Obama than they otherwise would be. This improved Mr. Obama’s overall vote share by a further 0.5 points…

Also, our study is measured in terms of the marginal effect on Mr. Obama’s vote. But the way that we have designed the analysis, any votes that did not go to Mr. Obama instead went to Senator John McCain. Therefore, the impact on the margin between the two candidates was twice as large: not 2.4 points, but 4.8 points.

This is fairly meaningful. Of the last 10 elections in which the Democratic candidate won the popular vote (counting 2000, when Al Gore lost in the Electoral College), he did so by 4.8 points or fewer on 4 occasions (2000, 1976, 1960, 1948). So, while the impact of union voting is not gigantic in the abstract, it has the potential to sway quite a few presidential elections, since presidential elections are usually fairly close.