Supreme Court Chief Justice John G. Roberts Jr. greets churchgoers as he leaves the Cathedral of St. Matthew the Apostle in Washington on Oct. 1. (Jose Luis Magana/Associated Press)

Chief Justice John G. Roberts Jr. has made it his mission to try to convince the American public that the Supreme Court is something unlike other Washington institutions — different from the gridlocked mess across the street in the Capitol, more disciplined and respectful of its place in the constitutional constellation than the bellicose White House down Pennsylvania Avenue.

The nine justices are not Democrats or Republicans, he often says, leaving unmentioned the political process that got each of them installed in their lifetime appointments. They put aside their personal and partisan preferences and go where the law and the Constitution lead them, he says.

Roberts, beginning his 13th year as the chief justice of the United States, is usually self-confident and sure-footed in his task.

But in the biggest political case of the Supreme Court’s term, Roberts’s actions opened him up last month more for criticism than praise. In the court’s examination of partisan gerrymandering, Roberts lamented the predicament the court would be in if called upon regularly to choose winners and losers among Democrats and Republicans.

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Critics on both the left and right called him out, saying it sounded as though he were more worried about polishing the court’s reputation than fulfilling its duty.

The case was about whether Wisconsin’s Republican legislative leadership had so gerrymandered the state’s legislative districts as to make GOP control inevitable and Democratic opposition practically futile. In the first election after the district lines were drawn, Republican legislative candidates got 48 percent of the statewide vote but captured 60 of 99 State Assembly seats.

The court’s decision could reshape the nation’s politics. Although the court has been vigilant about guarding the redistricting process against racial gerrymandering, the justices have never rejected a state’s plan because it was too partisan.

Roberts was skeptical that the court had a role to play, because the political redistricting process might belong exclusively to the people’s elected representatives. That is not so unusual — the last time the court considered the issue, in 2004, four of the nine justices said the court should stay out of partisan redistricting.

And Roberts was also leery of the mathematical test challengers had come up with to try to measure when normal politics became unconstitutional bias. (One version is called the “efficiency gap,” or EG.) That’s not so unusual, either. There are plenty of skeptics of the plan.

But Roberts’s real objection seemed to be that forcing the court to make such decisions would put the justices in a no-win position and tarnish the reputation that they — he — had worked hard to burnish:

“We will have to decide in every case whether the Democrats win or the Republicans win. So it’s going to be a problem here across the board. And if you’re the intelligent man on the street and the court issues a decision, and let’s say, okay, the Democrats win, and that person will say, ‘Well, why did the Democrats win?’ ”

The answer that a mathematical test found a way to gauge when partisan gerrymandering was too prevalent will not be convincing, Roberts said.

“The intelligent man on the street is going to say that’s a bunch of baloney. It must be because the Supreme Court preferred the Democrats over the Republicans. And that’s going to come out one case after another as these cases are brought in every state. And that is going to cause very serious harm to the status and integrity of the decisions of this court in the eyes of the country.”

As quickly as anyone could say Bush v. Gore, or Citizens United v. Federal Election Commission, criticism came from both left and right.

“Wait,” the conservative blogger Jennifer Rubin wrote in The Washington Post. “Especially for a ‘conservative’ justice, where does it say in the Constitution that the court should ‘ignore constitutional violations if it makes the court less respected by people who don’t read opinions’? This is an entirely illegitimate concern.”

Joseph R. Fishkin, a University of Texas law professor writing on the liberal legal blog Balkinization, said he had a “simple and realist answer” for Roberts: “That thing you are worried about, where the Court’s intervention is perceived as partisan and thereby erodes respect for the Court? It is not going to happen.”

More likely, Fishkin wrote, is that Roberts’s imaginary intelligent man on the street will say: “What a bunch of baloney. The Court is refusing to fix this problem even though they’re the only ones who can fix this problem. I guess they are part of the problem.”

There was more.

In expressing his skepticism of the test the challengers said the court could use to decide when a redistricting plan became an outlier, Roberts went a little far in his self-deprecation.

“The whole point is you’re taking these issues away from democracy and you’re throwing them into the courts pursuant to — and it may be simply my educational background, but I can only describe as — sociological gobbledygook,” Roberts said.

No one has ever doubted Roberts’s brain, and it’s unlikely the Harvard graduate who dazzled at Harvard Law School was underserved by his professors.

Paul Smith, the attorney for the challengers, responded, “Your Honor, this is — this is not complicated.”

Justice Elena Kagan served up the droll observation that if state legislators could use enhanced voter technology to draw maps to lock in majorities for election after election, surely judges could use the same techniques to determine when those plans had gone too far.

And the American Sociological Association weighed in on Roberts as well, in a somewhat snooty letter released publicly.

We “are particularly concerned about a person of your stature suggesting to the public that scientific measurement is not valid or reliable and that expertise should not be trusted,” wrote Eduardo Bonilla-Silva, the association’s president. “What you call “gobbledygook” is rigorous and empirical.”

He added, “Should you be interested in enhancing your education in this area, we would be glad to put together a group of nationally and internationally renowned sociologists to meet with you and your staff.”

That doesn’t seem likely.

Roberts, of course, has a point. The Supreme Court has a mandate from Congress to review decisions about redistricting from the lower courts and either affirm or reverse those decisions. The court in recent years has been drawn into redistricting battles in Alabama, Arizona, Maryland, North Carolina and Texas.

If the court decides charges of partisan gerrymandering should receive the same scrutiny as charges of racial gerrymandering, there will no doubt be more challenges making their way to the high court.

Justice Anthony M. Kennedy, 81, probably holds the deciding vote in the case. But he may not be around to review the redistricting challenges that would follow the 2020 Census.

It would be Roberts and the court he heads that would be left to apply the gobbledygook and avoid the baloney.