The unexpected death of Associate Justice Antonin Scalia left the United States Supreme Court with only eight justices. The Senate majority leader, Mitch McConnell, has made it clear that the Senate will not consider holding hearings or voting on President Obama’s nominee, Merrick Garland, until after the presidential election.

In the meantime, what happens to the cases already on the Supreme Court’s docket?

As many commentators have pointed out, the court may be evenly divided on a number of important cases. In those 4 to 4 cases, the lower appellate court decision will stand but will not set national precedent or policy. Or the court could hold over such cases for reargument until next term when the court is more likely to be fully staffed. Some knowledgeable court watchers think that’s what will happen for many or all 4 to 4 cases this term.

What’s happened in past Supreme Courts?

Are they right? We tested this proposition based, in part, on our previous research about rearguments. Using the Supreme Court Database, we tracked how many cases have been reargued since 1946 and whether the rate of reargument increased when the court had vacancies.

Our analysis suggests that court vacancies in the middle of a term may lead to one of two results. First, if the court has not yet heard oral arguments in a case (as is true of Whole Woman’s Health v. Hellerstedt), the court will most likely move forward with the case as normal: hearing oral arguments, voting in conference, drafting and signing opinions, and announcing a decision.

Second, if the court already heard oral arguments in a case (as is true in Friedrichs v. California Teachers Association), the now-absent justice’s vote no longer counts. That’s really a problem if the vote was close or if that justice was writing the majority opinion. If that’s true, the opinion must be reassigned to a different justice, who may have a different idea of how the opinion should be reasoned.

Either way, the case might be decided 4 to 4. The justices would have an incentive to push the case to the next term, hoping that a new justice can resolve the tie.

But the second scenario is more likely to upset the court’s internal workings — and therefore motivate the justices to hold the case over. In other words, we started our research with the hypothesis that cases are most likely to be pushed to the next term if a justice leaves the court after that case’s oral argument.

If a justice leaves the court after a case has been argued, does that boost the likelihood that the court will push it off till next term?

The figure below shows the number of reargued cases from 1946 to 2014, denoted by the dark line. As you see, vacancies are indeed associated with reargued cases. Specifically, the bars show the number of cases decided in each term after the court lost a justice, either before (dark gray bars) or after (light gray bars) oral argument. Clearly, the rise and fall of reargued cases closely tracks the spikes in vacancies.

We tested the strength of this relationship with a model that controls for other important factors, including the type of legal issue at question in a case and whether that issue is a salient one. Holding all else equal, our model estimates that, when a vacancy occurs before it’s been argued, the probability that the justices will choose to reargue the case increases from 1.3 percent to 4.6 percent.

Even more important, as we hypothesized, the probability jumps when a justice leaves the court after a case was already argued. That situation increases the probability the court will rehear the case from 1 percent to 15.6 percent.

So how many cases should we expect the Roberts court to put off till next term?

In other words, when a justice leaves the court, the odds that a case will be reargued jumps from a miniscule probability to a small-but-not-inconsequential probability. So how many cases from this term should we expect to see pushed to next term?

Here’s how we figured that out. We counted 24 cases on SCOTUSblog in which the court already heard oral arguments but hadn’t issued a decision before Justice Scalia’s death. We also found 51 cases in which the court hadn’t heard oral argument before he passed. If this were a normal term, we’d expect six cases to be pushed out to next term: about four cases from the first group and two from the second.

But this isn’t a normal court or a normal vacancy.

There aren’t any official rules for how the court decides to reargue a case. But our earlier research shows that justices typically hold over cases only if a majority of five justices agree to do so. The problem is that, given this court’s ideological divisions and the unusually contentious nomination battle, it’s hard to picture five justices agreeing to reargue any cases.

It’s all complicated by the rule of five

Let us explain. Most political science research on the court assumes the justices act strategically to achieve policies that are most similar to their own ideological preferences – for instance, when a justice joins an opinion that is not the exact policy she would prefer but that is better than the next most likely alternative.

So what would be the most strategic thing for the current justices to do? The court is currently split between four left-leaning justices and four right-leaning justices. All eight know that, in the coming months, one of two things will happen:

  • A liberal/moderate justice will fill Scalia’s seat if either Garland is confirmed or if a Democratic president appoints a replacement in 2017.
  • A conservative justice will fill Scalia’s seat if the Senate Republicans successfully block Garland’s appointment and a Republican wins the White House in November.

If the justices think the first scenario is more likely, why would Kennedy or his three more conservative colleagues vote to reargue? That would give a new liberal majority the chance to draft an opinion that sets nationally binding precedent. If the justices think the second is more likely, none of the liberal justices have an incentive to vote to reargue, for the same reason.

After all, if this court decides these 4 to 4 cases, what’s the worst that could happen, in any individual justice’s mind? The court could affirm a decision and preserve a policy with which that justice disagrees — but only for one state or circuit without changing national policy. In other words, a 4 to 4 decision might not be any justice’s favorite choice — but it could still be better than the next most likely alternative.

So expect more 4 to 4 decisions than reargued cases — at a high cost

Thus, despite the massive increase in the probability of cases being reargued if a justice vacates the bench after oral arguments have been heard, if the justices all share similar predictions about what will happen to Scalia’s seat, and if they all behave cautiously and strategically, we should see significantly more even splits than reargued cases under the present circumstances. That includes potential tie votes in Whole Woman’s Health and Friedrichs.

Specifically, here’s what we expect. Important legal questions will go unresolved while we wait for a ninth justice. Texas’s abortion law, which includes provisions that might reduce the number of abortion clinics in Texas (and is the issue in Whole Woman’s Health), would stay on the books in the Fifth Circuit. Further, the union fees debated in Friedrichs would still be collected throughout the Ninth Circuit. In both cases, national decisions would have to wait for another case to reach the High Court sometime in the future.

Practically, the economic costs associated with a host of 4 to 4 decisions are real and quite high. Thanks in part to the rise of an elite Supreme Court bar, the cost of hiring attorneys to litigate cases at the Supreme Court can exceed $100,000 per case. And that doesn’t even count how much it costs third parties to draft and submit amicus briefs. Split decisions will mean legal teams have wasted resources amounting to millions of dollars — wasted, since the result is the same as if the court had simply refused to hear the case.

Of course, our conclusion that the court will ultimately reargue few cases from this term assumes that the justices are motivated primarily by their policy preferences and strategic calculations. Some justices might instead prefer to avoid equally divided cases. If that’s true, a justice might vote to put off a case until next term even if that means she won’t agree with the eventual result.

So what will this court do? Whatever it may be, its choices will teach us a great deal about how it makes decisions, what motivates the justices, and whether they’re any good at predicting the outcome of presidential elections.

Tom Pryor is a graduate student in political science at the University of Minnesota.

Timothy R. Johnson is Morse Alumni Distinguished Professor of Political Science and Law at the University of Minnesota.

Valerie Hoekstra is an associate professor of political science in the school of politics and global studies at Arizona State University.