They found that when the more extreme candidate won the primary, the party did far worse in the general election: Its share of votes fell by between 7 and 15 percentage points.

In addition, a greater proportion of the people who turned out to vote were members of the opposite party. So, say a more extreme Democrat barely defeats a moderate in the primary. The research suggests that the Republican share of voters who turn out would be 5 to 10 percentage points greater than if the moderate had been nominated — and that the Democrats are much more likely to lose because they nominated the more extreme candidate.