WASHINGTON — In a reversal of the usual worries about political influence on electoral map-making, the Supreme Court is being asked to let raw politics play an even bigger role in the drawing of congressional district boundaries.

The court hears argument Monday in an appeal by Republican lawmakers in Arizona against the state’s voter-approved independent redistricting commission for creating the districts of U.S. House members. A decision striking down the commission probably would doom a similar system in neighboring California, and could affect districting commissions in 11 other states.

The court previously has closed the door to lawsuits challenging excessive partisanship in redistricting, or gerrymandering. A gerrymandered district is intentionally drawn, and sometimes oddly shaped, to favor one political party.

Independent commissions such as Arizona’s “may be the only meaningful check” left to states that want to foster more competitive elections, reduce political polarization and bring fresh faces into the political process, the Obama administration said.

The court fight has one odd aspect: California Republicans are rooting against Arizona Republicans.

If the Republicans who control Arizona’s Legislature prevail, the process for drawing district lines in California for the nation’s largest congressional delegation, with 53 members, would returned to the heavily Democratic Legislature. Three former California governors, all Republicans, filed a brief with the court defending the independent redistricting commission that voters created in 2008.

California’ GOP chairman, Jim Brulte, though officially neutral, said “most of us understand that this could have a negative effect on Republicans in California.”

“Redistricting is perhaps the most political activity that government can engage in and a partisan gerrymander of the congressional seats could lead to more Democrats in Congress from California,” he said.

But Paul Clement, the lawyer for the Arizona Legislature, said the likely differing outcomes in Arizona and California demonstrate that the issue is not partisan.

“An unelected commission may benefit Republicans in one state and Democrats in another. But that simply underscores that once congressional redistricting is taken away from the state legislatures and given to another entity, there is no guarantee that such an entity will be neutral, or favor one party, or reflect the will of the people. Whatever their shortcomings, state legislatures are elected, politically accountable and hand-picked” by the Constitution’s authors for the map-drawing task, Clement said.

The argument against independent commissions rests in the Constitution’s Election Clause, which gives state legislatures the power to set “the times, places and manners of holding elections for senators and representatives.” It also allows Congress to change those plans.

The case could turn on whether Congress did so in a law passed in 1911, around the same time it was considering Arizona’s statehood. The justices also will weigh whether the Legislature even has the right to sue over the commission’s maps.

Only Arizona and California essentially remove the legislature from the process, the National Conference of State Legislatures said in support of the Republican lawmakers in Arizona.

Lawmakers’ only contribution in those states is picking commission members from a list devised by others. In the other states — Connecticut, Hawaii, Idaho, Indiana, Iowa, Maine, Montana, New Jersey, New York, Ohio and Washington — lawmakers either get first crack at drawing districts, approve plans drawn by commissions or appoint commission members of their choosing, the conference said.

Supporters of the commissions point to more competitive races in both Arizona and California since the commissions were created.

“When the district-drawing process is controlled by elected officials, the result too often is a process dominated by self-interest and partisan manipulation,” political scientists Thomas Mann and Norman Ornstein said in court papers in support of the independent commission.

States are required to redraw maps for congressional and state legislative districts to account for population changes after the once-a-decade census.

Arizona voters created their independent redistricting commission in 2000 after complaints that the Legislature was gerrymandering districts to keep one party or one member of Congress in office. The five-member commission has two Republicans and two Democrats, chosen by legislative leaders from a list drawn up by the state’s Commission on Appellate Court Appointments. Those four members then choose a political independent to be chairman.

The first crack at redistricting after the 2000 census pleased Republicans, and they did not sue. Democrats did, though unsuccessfully. But after the 2010 census, Republicans were unhappy with the commission when it left Republicans with four safe congressional seats, Democrats with two, and three tossup districts.

The three tossup seats all went Democratic in the 2012 election, but one turned Republican in 2014.

State Senate President Andy Biggs, a Republican, said the suit that resulted is not meant to ignore the will of the voters.

“I would like to make this very, very clear for people who look at this — this isn’t the will of the people, these lines,” Biggs said. “These are unelected people, they are appointed people, they are now, we know, not even held accountable to elected people. These people who draw these lines are the most … detached, tyrannical people, because it all boils down to one person. And that will be the chairman of the commission.”

Democrats, naturally, disagree.

“The bottom line is they had no problem with the independent redistricting law when the lines were drawn to their liking,” said Sen. Steve Farley, the assistant Democratic leader. “They’re having problems and suing to overturn it now that the lines weren’t drawn to their liking. And that’s frankly not fair and frankly not legal.”

A decision in Arizona State Legislature v. Arizona Independent Redistricting Commission, 13-1314, is expected before July.