The argument against that map can be traced to the most significant decision on political boundaries: the Supreme Court’s ruling, in 1964, that political districts must contain roughly equal numbers of people. (In the state at issue, Alabama, some State Senate districts contained as many as 41 times the number of voters of others.) Every vote must carry equal weight, the court stated; to dilute some voters’ voices by packing them into more populous districts violated the Equal Protection Clause of the Fourteenth Amendment.

That one-person-one-vote debate, which began two years earlier with the landmark case Baker v. Carr, was among the most fractious of the 20th century because the dissenters saw it as a disastrous intrusion into the domain of legislators — a “political thicket” that would inevitably politicize the court.

Now the court is as politicized as any in memory, cleaved into four reliably liberal justices who presumably favor limits on gerrymanders and four conservative justices who may want to let politicians decide. One justice — Anthony M. Kennedy, nominated by President Ronald Reagan and seated in 1988 — has denounced partisan gerrymandering but has wondered aloud whether the court could find a way to remedy it.

In the Wisconsin case, the plaintiffs — a band of Democrats backed by local lawyers and an advocacy group, the Campaign Legal Center — seek to expand the one-person-one-vote principle to partisan gerrymanders. By drawing a legislative map that effectively guarantees Republican victories in many Assembly districts, they say, Republican legislators rendered Democratic votes worthless, or at least worth less than Republican ones. That violates not only the Equal Protection Clause, they contend, but also the First Amendment, because it amounts to government-ordered punishment of Democrats for expressing their political preference at the ballot box.

The arguments are not new. The court itself has agreed that some partisan gerrymanders could violate the Equal Protection Clause. But it has also agreed that drawing political boundaries is unavoidably a political job and that some amount of partisanship is acceptable.

That makes the real question — the one that has tied the court in knots for three decades — tougher: Can the justices devise a yardstick that reliably measures when a gerrymander oversteps constitutional bounds? Or would that overstep the court’s own bounds and plunge it deeper into the political thicket of legislative duties?

Opponents of gerrymanders say the answer is clear. “The court can construct a cause of action that reliably flags extreme partisan gerrymanders, while placing meaningful constraints on judicial intervention,” the Brennan Center for Justice at the New York University School of Law argued in its brief. “Precisely because extreme partisan gerrymandering subverts normal politics, it cannot be addressed by normal politics.”