Study: tough primaries really do hurt in the general election

Every hard-fought primary provokes the question: Is this good for the party, energizing supporters and engaging the public with the race, or does the infighting just make everyone look bad?

It's hard to gauge the impact on presidential campaigns because there haven't been enough contested races in the brief history of presidential primaries for a statistically valid sample. But a new paper on primaries for Congress and state legislatures by Oxford's Alexander Fouirnaies and Stanford's Andy Hall suggests tough nomination battles really do hurt — and the authors see it as terrible news for Donald Trump in the fall, somewhat mitigated by the fact that Democrats also have a tough race.

Fouirnaies and Hall find close primary races that go to runoffs cost their parties a whopping 6 to 9 percentage points come November, and reduce their odds of victory by 21 percentage points.

What's more, they find that the effects grow with the importance of the office. In state legislatures, contested primaries don't hurt at all and even help in some cases. In US House races, they hurt a bit, and in US Senate races they hurt a lot.

Obviously it's hard to draw firm conclusions about the presidency from this, but Hall says these numbers at least imply that contentious primaries would hurt presidential candidates in the general election. "Given that the effects are increasingly negative the more salient the office," he tells me, "it suggests there would be big penalty for president."

Now, the Democratic race was also somewhat contentious, which may mitigate any effect of the bitterness of the GOP race. But it's difficult to dispute that the GOP race was more bitter — and if Fouirnaies and Hall's results really are extendable to presidential races, that bodes ill for Donald Trump.

The strategy: Look at runoffs

The tricky thing with a study like this is that you need to be able to distinguish contentious from non-contentious primaries. So Fouirnaies and Hall zero in on nine states (all in the South) where party primaries employ runoffs. In those states, first-place primary finishers below a given threshold (50 percent in every state but North Carolina, 40 percent there) face another election a few weeks or months later, against their second-place opponent.

So the contentious primaries are the ones that make it to a runoff, and which therefore involve significantly more campaigning.

To help control for other factors, Fouirnaies and Hall exploit the 50 percent threshold and compare races that just barely made it to a runoff (with, say, 49 percent of the vote going to the top placer) with ones that just barely avoided a runoff (with, for example, 51 percent). The two sets of cases are, apart from the presence of a runoff, pretty similar; they both feature frontrunners of roughly equal strength. The main difference is the runoff campaign period. That allows Fouirnaies and Hall to estimate that period's effect on the general election:

Fouirnaies and Hall 2016

They estimate the overall effect of runoffs as 6- to 9-point reduction in vote share and 21-point reduction in odds of victory.

Fouirnaies and Hall are jumping into an area with a large existing literature, which is often contradictory. While some papers agree that candidates emerging from contentious primaries do worse (except in state legislature races), others find no effect. The advantage of their paper is its uniquely strong methodology. The runoff threshold allows Fouirnaies and Hall to use what social scientists call a "regression discontinuity" design, which can be nearly as good as using randomized experimental evidence. That gives some reason to be confident in their results.

The authors aren't shy about what this might mean for Donald Trump. "No doubt, it is tempting, too, to extrapolate these results and use them to predict the current presidential election," Fouirnaies and Hall write. "Clearly, the Republican primary has been historically divisive, and the whole world has been watching. As such, we would expect a substantial penalty to the party in the upcoming general election. On the other hand—and conveniently this allows us to hedge our bets a little—the Democratic primary has also been quite competitive."

In any case, the results are certainly applicable in Southern states' House and Senate primaries. Take Florida, a state that used to have a runoff system and is now in the middle of a contentious Senate race. Both parties' nominations are contested, but the race between Reps. Patrick Murphy (D-FL) and Alan Grayson (D-FL) on the Democratic side is particularly heated. The Fouirnaies/Hall research suggests that could wind up harming Democrats' odds of retaking Marco Rubio's seat.

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