A legal world that promoted originalism would generate greater stability.
There is a long established convention of referring to the Supreme Court in a given era by the name of its Chief Justice. Thus, we have the Marshall Court, the Warren Court, and the Rehnquist Court. But this name is often a misnomer because the Chief was not the most influential member of his Court. Like all other justices, he always has but one vote. Particularly in the modern era, where political scientists can evaluate judges based on ideological scores, the better name for a Court might that of the swing or median Justice. Under this view, we are living currently in the era of the Kennedy Court.
But probably not for much longer. Justice Anthony Kennedy has announced to prospective clerks that he thinking of retiring. Moreover, as I have previously discussed, with rise of partisanship, justices now have every incentive to retire when both the Presidency and the Senate is under the control of the party whose President appointed them. Otherwise the Court may be left short-handed for an indefinite period and they may be replaced by justices of the opposite party when that alignment finally occurs. Kennedy cannot be confident that the Republicans will control the Senate after 2018.
Assuming that, as is likely, Kennedy is replaced by a justice with views like Neil Gorsuch, the Roberts Court will actually become the Roberts Court in more than name, because the Chief Justice will also become the median justice. That will make the Chief Justice the most powerful and pivotal Chief in modern times. Justices, like all political actors, tend to like power and there is some indication that the Chief is encouraging Justice Kennedy’s retirement. It has been widely remarked that Chief, alone among the dissenters in Obergefell, did not join in the dissent from Pavan v. Smith, but no one to my knowledge has put his action in the context of encouraging Justice Kennedy’s retirement. But that decision summarily reversed the Arkansas Supreme Court case which allowed the state to treat same-sex couples differently when issuing birth certificates. Roberts’ action can be interpreted as a signal to Kennedy that he will not roll back same-sex marriage rights, whatever the views of his fellow conservative justices. Kennedy correctly regards his homosexual rights decisions (Evans, Lawrence as well Obergefell) as the legacy by which he will be known to history. With that legacy secure, he will be ready to retire.
It is safe to venture a few predictions about the coming Roberts Court. First, it is likely that the Chief Justice will move somewhat to the left. He is an institutionalist and will be very concerned about 5-4 splits when all Republican appointed justices vote in the majority and all Democratic appointed justices in dissent. He thus will prioritize the issues that are worth dividing the Court. On the basis of past votes, those issues likely include limiting affirmative action and substantive due process but expanding the rights of speech and religion. But I would be skeptical that the Chief Justice will substantially limit federal legislative power, particularly when major legislation is at stake. When he is the pivotal vote, particularly with other Republican appointed justices, he will try to craft narrow opinions. Look to Justice Samuel Alito, similar in methodology, to get the greatest share of important opinions other than the Chief. Even in areas the Chief cares about he will look to move the Court to incremental change through common law methods rather than through the grand pronouncements, like those of his predecessor median justice.