As battles rage over the independence of the judiciary and whether one political party has claimed partisan control of the third branch of government, the state of Delaware says it has a better idea.

For more than a century, the state has required its major courts be roughly balanced, so that no more than a bare majority of a court is made up of members of one political party. And then it required the minority be made up of the other political party.

The result, Stanford law professor Michael W. McConnell told the U.S. Supreme Court Monday, is that “Delaware’s courts are widely regarded as the least partisan and most professional in the nation.”

The problem, countered Wilmington, Del., lawyer David L. Finger, is that it is unconstitutional. The plan denies the chance for his client, lawyer James Adams, to serve on the courts because he is neither a Democrat nor Republican but a political independent, Finger said, and that violates his First Amendment rights of political association.

It seemed a fitting beginning for the Supreme Court’s new term, as the Senate is torn along partisan lines about whether to confirm just before the election President Trump’s nominee Judge Amy Coney Barrett to replace Justice Ruth Bader Ginsburg, who died Sept. 18.

Ginsburg’s death left the court with five conservative justices, all named by Republican presidents, and three liberals named by Democrats. Barrett’s confirmation would install a 6-to-3 majority for conservatives.

That reality was unspoken, as the justices again gathered by teleconference to begin their traditional first-Monday-in-October arguments. As a concession to their scattered whereabouts, the marshal omitted the command in the familiar “oyez, oyez” cry that listeners should “draw near” to hear the business of the court.

Chief Justice John G. Roberts Jr. began the session by noting that the door and Ginsburg’s spot in the empty courtroom are hung with black crepe.

“Justice Ginsburg’s contributions, as advocate, jurist and citizen, are immeasurable,” Roberts said before the session began. “We at the court will remember her as a dear friend and treasured colleague.”

The Delaware case raised intriguing questions, but the court’s first order of business was whether Adams had the legal standing to raise them. A former Democrat who became an independent because he identifies more with Sen. Bernie Sanders (I-Vt.), Adams did not actually apply for a judicial opening. He said there was no point in doing so because of the Republican or Democrat requirement.

But McConnell said two of the state’s five levels of court do not have the partisan requirement, and Adams would be better suited for one of those anyway.

“He’s really interested here in pursuing a theory that he read about in a law review, not really getting a judgeship,” McConnell said.

That seemed to some justices an appealing way to get rid of the case. But others agreed with Finger there was no reason to force Adams to apply for a judgeship he could not get just to challenge the policy.

On the merits, Justice Stephen G. Breyer wondered about how a state could condition application for a judgeship on membership in one of the two major political parties.

“How do you get around the fact that the way that it’s written and applied is you have to be a Republican or a Democrat? And there are other parties,” Breyer said. “And so why is that constitutional?”

Justice Clarence Thomas asked if a state could mandate that all members of a court be of one party. McConnell said that would be problematic.

Justice Neil M. Gorsuch said eliminating independents from service was “quite a sweeping rule.” And Justice Brett M. Kavanaugh wondered about its wisdom, given Delaware’s goal.

“Why can’t independents even better serve the goal of a balanced judiciary nonpartisan/bipartisan judiciary?” he asked.

McConnell responded that the provision “is not really about whether independents can do a good job as judges.” It’s about limiting the governor’s discretion in making judicial appointments so that the courts remain balanced, McConnell said.

“It’s very odd to say that the [state] constitution cannot direct the governor in his exercise of discretion,” he said.

Finger appealed to the court’s own statements that the political affiliations of judges do not affect their actions on the bench.

Delaware’s restrictions are “based on the assumption that a judge’s political affiliation is determinative of how that judge will vote in a case,” Finger said. “And this court can look to its own history as a refutation of that premise. If this court accepts the premise, it’s the end of the idea of an independent judiciary.”

McConnell rebutted that in an answer to Justice Sonia Sotomayor, who made a similar point.

Partisan affiliation is “universally used by political science and scientists as the proxy for a philosophy and ideology, and it’s especially true now in the last . . . 20 or 30 years,” said McConnelll, a former federal judge named to the bench by President George W. Bush.

The parties have been through “what they call partisan sorting, so that today the most liberal Republican is — is at least similar to but, you know, probably more conservative than the most conservative Democrat,” he said.

The case is Carney v. Adams.