With the death of Justice Antonin Scalia on Saturday, Washington’s focus turns to the vacant seat on the Supreme Court. President Obama has pledged to nominate a candidate. In turn, Senate Republicans have pledged not to act on that nomination, arguing that it should wait until after the November presidential election.

But could Obama nominate someone who is attractive enough to a majority of senators that the Senate might, in fact, act? If so, here’s how it might work.

Research by political scientist Keith Krehbiel argues that success in Congress depends on the ideology of the “pivotal” member of the legislature. For example, the 51st-most-conservative (or liberal) senator is the pivotal voter if you need a majority to win. If you need to defeat a filibuster, the pivotal senator is the 60th-most-conservative (or liberal).

What does this mean, then, for the upcoming nomination to the Supreme Court? I used data from Voteview to determine the ideological scores of all 100 senators, as well as Obama and many current presidential candidates. I combined this with data from the Judicial Common Space project, which measures the ideology of Supreme Court justices in a way that allows for comparisons between the court, Congress and the President.

Scalia is scored as a 0.41 on this scale, which ranges from -1 (most liberal) to 1 (most conservative). He was the third-most-conservative justice on the court, behind Samuel Alito and Clarence Thomas. Interestingly, Scalia’s ideology score is identical to that of Senate Majority Leader Mitch McConnell, who is more conservative than 63 of his 99 Senate colleagues.

Looking forward to Obama’s nomination decision, the pivotal politics theory suggests that his best way forward is to nominate somebody who is ideologically similar to the 51st-most-liberal senator. In the current Congress, this person is Mississippi Republican Thad Cochran, who has been in the Senate since 1978. With an ideological score of 0.29, Cochran ranks as the fifth-least-conservative Republican in the Senate.

If Obama needed to avoid a filibuster, he would need to appease the 60th-most-liberal Senator: Tennessee Republican Bob Corker. Corker’s ideological score is 0.39 — making him slightly more conservative than Senate Judiciary Committee Chair Chuck Grassley and slightly more liberal than Mitch McConnell.

In either of these two scenarios, Scalia would be replaced by a justice who is slightly more liberal, pushing the balance of the court to the left.

Of course, Obama would prefer to nominate somebody significantly more liberal than that. Presidents routinely choose nominees whose views are closer to their own or to those of the average members of their party, rather than those of pivotal members of the opposite party.

In that case, these data show just how difficult such a move would be. Even if Obama picked somebody between Stephen Breyer and Anthony Kennedy — a new “swing vote” on the court — Republican Senators would need to be convinced based on more than just the nominee’s ideology. The president would have to pick someone with excellent qualifications and no political skeletons, and hope for the best.

Right now, however, it looks as if the court could have a vacancy for months to come.

Stephen Pettigrew is a PhD. student in the Department of Government at Harvard University.