Perhaps more strikingly, the judges ruled that all 34 maps violated Democratic voters’ First Amendment right to freedom of association and effectively punished them for their political views by placing them in districts where their votes were worthless. Plaintiffs in the North Carolina gerrymander case made the same argument to the Supreme Court in March.

In each of the contested districts, the judges wrote, the plaintiffs — the League of Women Voters, representing individual Michigan citizens — proved that the legislature had intended to silence Democratic voters, that the maps succeeded at that task, and that there was no other reasonable justification for the way the maps were drawn.

The judges rejected the contention by lawyers for the legislature that the maps simply adhered to state standards that lawmakers were required to follow when drawing political boundaries — that districts have nearly the same population, for example, and that the mapmakers try not to split counties and cities. “The evidence points only to one conclusion: partisan considerations played a central role in every aspect of the redistricting process,” the judges wrote.

In elections from 2012 through 2016, they noted, Michigan Republicans won nine of the state’s 14 House seats — 64 percent — despite failing to win more than 50.5 percent of the statewide vote in any of those years. And last year, when Democrats won nearly 56 percent of the vote and swept statewide offices, they still won only half the 14 House seats.

The legislators’ case was undermined early on by a string of emails unearthed during discovery that laid bare both their intentions and the political animus behind them. The emails boasted of packing “Dem garbage” into four districts in southeastern Michigan, leaving adjacent districts with secure Republican majorities. And the messages joked over how a narrow extension of one Democratic congressman’s district was “giving the finger” to its incumbent.

Another 2011 email noted that Republican Party experts, who earlier had mounted a nationwide campaign to capture state legislatures and control redistricting, had created a congressional map for Michigan that would increase the party’s share of seats in the state to 10 out of 14. But a state Republican strategist rejected that map, saying that “we need for legal and P.R. purposes a good-looking map” that did not “look like a gerrymander.”

The judges appeared most swayed, however, by stacks of statistical evidence that the 34 House and legislative districts so profoundly benefited Republicans that there was no plausible explanation for their shapes beyond locking in a partisan advantage.