Hang on to your hats, New Yorkers. That’s the word in the wake of this week’s decision of the United States Supreme Court to take a new look at the meaning of the constitutional mantra of “one man, one vote.” It could ignite an earthquake in American politics.

The case — known as Evenwel v. Abbott — is arising from Texas. It’s about whether voting power has to be apportioned equally by general population or by eligible voters. The impact could extend way beyond the Lone Star State, shifting political power away from cities.

Particularly cities with relatively high, non-voting immigrant populations like — oh, say — New York. The case has the potential to require authorities to strip away during the redistricting process population that isn’t eligible to vote — undocumented aliens, felons, children.

Edward Blum is the conservative constitutional sage who heads the Project on Fair Representation, which provided counsel in this case. He tells me the Nine could force redistricting. The court could, he said, “help upstate New York districts dramatically.”

Not just upstate. Mr. Blum reckons the case could lead to changes in city councils, too. He speculates that council districts in such big cities as New York, Houston and Chicago are among the “most mal-apportioned” in the country.

It’s unclear how directly affected United States congressional districts might be, because of language in the Constitution. But Mr. Blum thinks Congresswoman Nydia Velázquez’s district, just to pick one out of the air, could be mal-apportioned by as much as 40 percent.

Mr. Blum cautions that the figure is speculative. He predicts that the court’s decision to hear the case will itself ignite a scramble for data as the implications become clear.

Slate.com is already suggesting that a victory by Mr. Blum’s clients — two Texas voters who feel under-represented — could mean “more Republican districts.” This is because most states apportion districts based on total population, which, Slate says, “includes noncitizens, children, felons and others ineligible to vote.”

The riddle the case attacks was left unsolved by the series of Supreme Court cases known as the one-man-one-vote decisions. The court started acting in the 1960s. In 1962, in Baker v. Carr, it ruled that federal judges could get involved in redistricting cases, even if they are political.

In 1964 the Supreme Court ruled, in Reynolds v. Sims, that state legislative districts had to be approximately equal in population. The opinion was penned by Chief Justice Earl Warren, who called state legislatures the “fountainhead of representative government in this country.”

“Legislators represent people, not trees or acres,” Warren wrote in a formulation that has echoed through the years. “Legislators are elected by voters, not farms or cities or economic interests.”

After one-man-one-vote, it was no longer constitutional to set up, say, a state senate that gave a rural county the same number of senators as an urban county. This is true even though at the federal level, the Constitution provides that a small state can never be denied representation in the United States Senate equal to that of a large state.

New York City itself eventually felt the reach of one-man-one-vote. That came in 1989, when the Supreme Court ruled that the Board of Estimate, which had governed our metropolis for a century, was unconstitutional, because populous Brooklyn had the same representation as sparsely settled Staten Island.

That led to a revision and empowerment of the city council. By the 1990s, New Yorkers were so disgusted with it that they brought in term limits to force the old guard out. If Evenwel prevails, there could be a new review of how the city council districts are laid out.

Is there a racial angle to this case? That’s not so clear. The NAACP has yet to be heard from — possibly, one scholar suggested to me, because the interests of the African-American community and the Hispanic community, which has more non-citizens, might not be entirely aligned.

What the plaintiffs in this case insist on is that there has to be a way to craft electoral districts so that both population and registered voters are fairly apportioned. Their appeal seems to suggest that this is a matter of commitment and hard work at governance.

The case is a reminder of that America is a constant struggle to get government right. This is the first purpose of the US Constitution, announced in the parchment’s preamble, where it declares the aspiration “to form a more perfect union.”

This column first appeared in the New York Post.