Let’s take a specific example of what this means in the case of a contentious issue like immigration, which continues to roil American politics. Despite a recent ugly rally and series of tweets from the president, the data show that, in fact, a strong majority of Republicans believe that properly controlled immigration can be good for the country. They also show that a strong majority of Democrats disagree that the United States should have completely open borders. In other words, while left and right differ on immigration, those holding extreme views are a minority in both parties. However, Republicans think a majority of Democrats believe in open borders while Democrats think a majority of Republicans believe immigration is bad for the United States. The perception gap is 33 percentage points on each side.
And that is the perception gap for the average Democrat or Republican. Strong partisans — progressive activists and devoted conservatives — are most inaccurate in their perceptions of the other side, reaching more than 45 percentage points on extremely divisive issues.