A dramatic hour at the Supreme Court on Tuesday left the most crucial question unanswered: Does Justice Anthony Kennedy believe that there is a clear method to identifying when a partisan gerrymander is so extreme that it is undemocratic and unconstitutional? The much anticipated oral arguments in Gill v. Whitford did make it clear that none of the four conservative Justices seems likely to be swayed by even the most simple and revealing tests.

Chief Justice John Roberts dismissed arguments against partisan gerrymandering as so much “sociological gobbledygook.” Justice Samuel Alito, while conceding that gerrymandering may be “distasteful,” brushed aside measures for preventing it as unmanageable, unreliable, or too confusing. The newest Justice, Neil Gorsuch, compared gerrymandering to his homemade turmeric steak rub: “A pinch of this, a pinch of that.”

The four liberal Justices, meanwhile, appeared eager to embrace what could be the Court’s best and final chance to set limits on a political party’s ability to use sophisticated technological tools to draw electoral maps in ways that would give it decade-long advantages in state legislatures and Congress. “If you can stack a legislature in this way, what incentive is there for a voter to exercise his vote?” Justice Ruth Bader Ginsburg asked. “The result is preordained in most of these districts. Isn’t that what becomes of the precious right to vote?”

This case emerged as a challenge to Wisconsin’s State Assembly districts, which were painstakingly drawn by Republicans in 2011 to maximize partisan advantage, and which have reliably delivered more than sixty per cent of the seats in the Assembly to the G.O.P., even in a year when Democratic candidates earned more votes. Justice Sonia Sotomayor asked how gerrymandering aided democracy, asking, “It’s O.K. to stack the decks so that for ten years, or an indefinite period of time, one party—even though it gets a minority of votes—can get the majority of seats?”

That leaves Kennedy as the decider, once again. It’s a familiar role: when the Court last considered partisan gerrymandering, in Vieth v. Jubelirer, in 2004, Kennedy made his disdain for the practice clear. However, as the swing vote on a similarly divided Court, he sided, reluctantly, with the conservatives. Kennedy found himself unsatisfied with the proposed guidelines for instructing courts or legislatures on how to separate one bad gerrymander from another—but he was open to future suggestions for standards.

Tuesday’s arguments, then, are best understood as an attempt by both sides to sway Kennedy. The liberal justices, along with Paul Smith, representing the plaintiffs, aimed to convince Kennedy that today’s standards are clearer than they were in Vieth, and that technological advances make gerrymandering more threatening to democracy. Justices led by Roberts, meanwhile, argued that the standards remain opaque and that it’s the Court’s integrity that would be threatened by interfering with the political process to apply them.

Kennedy, predictably, did not tip his hand, but he did leave some clues. He saved his questions for the Wisconsin attorneys defending the G.O.P. maps, and one question in particular appeared to show that he was casting toward the “limited and precise” constitutional standard he sought in Vieth. “Suppose a state constitution or state statute says all districts shall be designed as closely as possible to conform with traditional principles,” he posed, “but the overriding concern is to . . . have a maximum number of votes for party X or party Y?”

While redistricting reformers advanced a quantitative test called the “efficiency gap” to satisfy Kennedy’s desire for an across-the-board measure, the liberal Justices suggested a more simple eye test. Justice Stephen Breyer posed a three-part standard that courts could examine. First, were the maps drawn under the control of just one political party? Second, do they overwhelmingly favor one side? Lastly, is there a durable advantage embedded in the maps that favors those holding the pens even when the other party gets more votes?

“I suspect that that’s manageable,” Breyer said, conceding that the “social-science stuff and the computer stuff” could be a “little complicated.” He added, “I throw it out there as my effort to take the technicalities and turn them into possibly manageable questions.”

Justice Elena Kagan emphasized the number of advanced tools that could uncover an extreme gerrymander—and that all such expert indicators agreed that Wisconsin’s maps were a dramatic outlier. “This is not kind of hypothetical, airy-fairy,” she said. “This is pretty scientific by this point.” If mapmakers use these extremely sophisticated tools, she argued, courts should also have them at their disposal to evaluate the constitutionality of district lines.

Conservatives, however, diminished the value of the political-science research. Alito marvelled that it had been thirty years since the Court opened the door to a standard for measuring gerrymandering, and said that the efficiency gap, full of “unanswered questions,” still seemed like a half-baked and unproven test. “If we are going to impose a standard on the courts, it has to be something that’s manageable, and it has to be something that’s sufficiently concrete,” Alito said.

Roberts warned that making dire predictions about uncompetitive elections and democracy’s death “on the basis of the statistics before us has been a very hazardous enterprise.” Gorsuch, meanwhile, compared all this to his secret grilling rub, suggesting that the various social-science measures being presented were slapdash and would be too challenging for lower courts to apply in a consistent manner. “I like some turmeric. I like a few other ingredients, but I’m not going to tell you how much of each. And so what’s this Court supposed to do? What is it that you want us to constitutionalize?”

Roberts then brought it all back to politics. The Court, he argued, would have to be the arbiter of whether maps too strongly favored Democrats or Republicans. And the average voter, he said, would always think that the Court had reached its decisions because partisan Justices were favoring one side or the other. “If you're the intelligent man on the street, and the Court issues a decision, and let's say, O.K., the Democrats win, and that person will say, ‘Well, why did the Democrats win?’ ” Roberts said. “And the answer is going to be because E.G.”—efficiency gap—“was greater than seven per cent, where E.G. is the sigma of party X wasted votes minus the sigma of party Y.” Roberts argued that Americans would simply feel that judges were skewing the electoral playing field. “The intelligent man on the street is going to say that’s a bunch of baloney,” he said. “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.”

Smith pleaded with Roberts to recognize the enormous threat to democracy that extreme gerrymandering represents. He asked the Justices to recognize that the Court is actually the last institution capable of solving the problem before more sophisticated data analytics and increasing polarization worsen gerrymandering in the 2020 redistricting cycle. “If you say . . . we’re not going to have a judicial remedy for this problem, in 2020 you’re going to have a festival of copycat gerrymandering the likes of which this country has never seen,” he said. “It may be that you can protect the Court from seeming political, but the country is going to lose faith in democracy big time.”

While Smith emphasized reasonableness and the ability to target only the most extreme maps, the conservative Justices repeatedly pressed him on how that could actually be done. Both sides had an audience of one in mind: Kennedy.

After the arguments, a buoyant and optimistic Paul Smith laughed and told me that, notwithstanding the Justices who had asked questions about “gobbledygook,” he wasn’t particularly concerned that the entire Court would frown upon any technical standard. “They like to throw up their hands and say, ‘Oh, it’s too complicated for me!’ ” Smith said. “The reality is, a number of Justices understood what the record very clearly showed—that this was a maximizing kind of gerrymander.”

Left unclear, and unsaid, after all this debate is whether that number of Justices is four or five. The future of our politics depends on which it is.