One way we can test the referendum theory is to see how well incumbents’ vote shares have lined up with their approval ratings. If the correlation is weak — if incumbents frequently receive the votes of those who disapprove of them, or frequently lose substantial numbers of votes of those who approve — then we might assume that either voters are engaging in a more abstract “choice,” or that the bar in Step 2 is so high that it effectively creates a choice election.

If, however, they line up nicely, and incumbents tend to pull in a vote share roughly similar to their approval rating, then we have a sense that the referendum model has legs to it. Now it might still be the case, as Kilgore at times suggests, that bashing an opponent raises the incumbent’s approval. But this is both hard to test and, in any event, fully consistent with the idea that, in the end, we’re left with a referendum on the incumbent, regardless of exactly how the incumbent arrived at his approval rating on Election Day.

Let’s start with the two major examples that Kilgore advances in support of his claim: The 1980 and 2004 elections. Both of these examples actually suggest the exact opposite of what he claims. In 1980, a majority of the electorate believed that Jimmy Carter was doing a poor job, and he lost. In 2004, a majority of the electorate believed that George W. Bush was doing a good job, and he won.