Sens. John McCain (R-Ariz.) and Sheldon Whitehouse (D-R.I.) asked the Supreme Court on Tuesday to uphold a lower court’s ruling that Wisconsin’s electoral maps for the state legislature were unconstitutional.

The senators made their argument in a friend of the court brief filed in Gill v. Whitford, a potentially monumental case the Supreme Court is set to hear on Oct. 3. The nation’s highest court has never said whether an electoral map, drawn by state lawmakers every 10 years ― often by the party in power ― can be unconstitutional simply for favoring one party too much over the other.

The Supreme Court could make such a determination in the Wisconsin case, which could remake American politics by requiring states to draw maps that put lawmakers in more competitive races.

In the brief, McCain and Whitehouse said the case “implicates the effective functioning of American representative democracy.”

Redrawing electoral maps to weaken the electoral influence of a particular group, often called gerrymandering, can now be done with extreme sophistication, using algorithms and complex software, the senators wrote.

“This new breed of ‘bulk’ partisan gerrymandering distorts statewide votes, systematically diluting the effect of votes based on political affiliation and leading to the election of congressional and state legislative delegations that do not represent the will of the voters,” they wrote. “This practice violates ‘the core principle of republican government, namely, that the voters should choose their representatives, not the other way around.’”

Both Republicans and Democrats have benefitted from gerrymandering, the brief notes. The progressive Brennan Center for Justice estimates that gerrymandering accounts for 16 or 17 current Republican seats in the House of Representatives.

In a 2004 case called Vieth v. Jubelirer, the court ruled 5-4 not to strike down Pennsylvania’s congressional maps as an unconstitutional gerrymander, and four justices wrote the Supreme Court couldn’t even hear the case. Despite voting with the majority, however, Justice Anthony Kennedy wrote that he believed a standard for determining whether a map was unconstitutional could in fact exist. Because of that opinion, Kennedy is being closely watched in the Wisconsin case and the plaintiffs are hoping he sees a standard that he likes.

The brief argues the court does not need to establish a comprehensive test in the Wisconsin case about gerrymandering. But it says that affirming the ruling of the lower court that the maps in that case were unconstitutional would send a strong signal about the Supreme Court’s attitude on the issue.

“The district court’s test provides a workable framework for distinguishing between district maps drawn based on legitimate political considerations and those constituting unlawful partisan gerrymandering,” the brief says. “Beyond remedying the constitutional violations present in this case, affirming the district court’s decision will send a clear message that partisan gerrymandering will not be tolerated.”

In a separate brief filed Tuesday, 65 current and former state lawmakers (26 Republicans and 39 Democrats) from eight states also asked the Supreme Court to uphold the lower court’s decision and say Wisconsin’s map was unconstitutional.

In the brief from McCain and Whitehouse, the senators noted that gerrymandering weakens confidence in the electoral system.

“Americans do not like gerrymandering. They see its mischief, and absent a legal remedy, their sense of powerlessness and discouragement has increased, deepening the crisis of confidence in our democracy. We share this perspective,” they wrote. “We see wasted votes and silenced voices. We see hidden power. And we see a correctable problem.”

More than three dozen current and former Republican lawmakers have signed onto briefs urging the court to say the Wisconsin maps were unconstitutional. The Republicans ranged across the political spectrum and included House Freedom Caucus Chairman Mark Meadows (N.C.), former California Gov. Arnold Schwarzenegger and Ohio Gov. John Kasich.

This article has been updated with more information about which GOP lawmakers have signed onto briefs.

CORRECTION: A previous version of this story misstated the state Mark Meadows represents in Congress.