Boris Shor, Andrew Gelman, and I have had a couple of exchanges about the role of "balancing" in the Georgia Senate runoff. Gelman is skeptical of balancing and stresses the importance of low turnout in runoff and special elections. The problem with turnout explanations (as I pointed out in my original post) is that it is hard to predict who benefits from a low turnout election.
I thought it might be useful to bring in a little bit of data on special elections. Fortunately, someone has compiled a list of special House elections and put it on Wikipedia. From WWII onward, the list contains 163 special House elections with the name and party of the winner and the previous holder of the seat. Of these elections, 95 were won by Democrats and 68 by Republicans.
The "balancing hypothesis" would predict that the president's party would do worse in these elections than the out party. Looking at all of these elections, the president's party lost 97 of the 163 (about 60%). For those of you who care, the p-value for the hypothesis that the president's party does no worse than the out party is just .03.
But looking at all special elections may underestimate the president's disadvantage. After all, many House districts are not competitive so the incumbent party will win easily no matter who is president. Ideally, I would collect data on district partisanship to use as a control. But that is too much work for a blog. So let's just look at the pattern of districts that switched from one party to another. In such cases, the president's party lost 29 seats and only picked up 11.
So I'm not wedded to the balancing hypothesis, but it seems to me any explanation about special and runoff elections ought to account for how poorly the president's party performs. Maybe there is a theory of turnout that does that, but I am unaware of it.