WASHINGTON (AP) — Groups hoping to squeeze partisan politics out of how states shape congressional districts are hailing a Supreme Court decision that lets independent commissions, not legislatures, draw those lines.

But Republicans say Monday’s 5-4 decision upholding Arizona’s independent redistricting commission will have little nationwide impact. And history shows that past efforts to persuade voters to change how states shape districts have had mixed results.

Proponents of shifting redistricting from state legislatures to independent bodies say they’ll rely in part on the same technique Arizona used: Initiatives, which let voters put questions on the ballot, usually after gathering signatures on petitions.

“The current system allows politicians to choose their voters, rather than allowing voters to choose their elected officials,” said Lloyd Leonard, advocacy director for the League of Women Voters, which filed a brief backing the commission.

From 1904 to 2001, there were 39 statewide ballot initiatives on how legislative boundaries are configured, and the voters have approved only 15, according data from the Initiative and Referendum Institute at the University of Southern California law school. Most addressed state legislative lines.

That underscores the difficulty of approving those changes and how infrequently such questions come before voters. Twenty-four states allow ballot initiatives, according to the institute.

While that opens the door for many states to consider redistricting commissions, “That door wasn’t exactly swinging wildly before this case came up,” said Thomas Mann, a congressional scholar at the liberal-leaning Brookings Institution who submitted a brief supporting commissions.

On Tuesday, the Supreme Court agreed to hear a new case in coming months on whether the drawing of state legislative lines by Arizona’s redistricting commission was constitutional.

With the GOP’s current House majority aided by its domination of congressional line-drawing in many states, some Republicans conceded that reducing that power could hurt them but would be hard for opponents to achieve.

“It’s a sweeping decision that lays the groundwork, but the work still has to be done” by advocates of independent commissions, said GOP strategist Sean Noble. “And whether they have the time, money or will has yet to be determined.”

Others doubted that commissions would actually remove partisanship from the once-a-decade process of shaping congressional districts.

The commissions “could be used to shield or really cover what is actually the same partisan politics,” said Michael T. Morley, attorney for the conservative Coolidge-Reagan Foundation, which wrote a brief opposing the Arizona commission.

Kathay Feng, national redistricting director for the liberal Common Cause, said efforts to use initiatives to alter how district boundaries are drawn are under way in Illinois, Michigan and Ohio. In three other states, supporters are working through the legislature: Indiana, Maryland and North Carolina, she said.

House Speaker John Boehner, R-Ohio, “believes redistricting decisions are best made by the people’s representatives in state legislatures — not by some unelected, unaccountable board of bureaucrats,” said Boehner press secretary Olivia Hnat.

House Minority Leader Nancy Pelosi, D-Calif., backed the court decision and said Congress should set standards so state redistricting commissions “reflect the diversity of their states and communities.”

In Monday’s ruling, the justices rejected a challenge by Arizona’s Republican-led legislature to the state’s independent commission, which voters established by ballot initiative in 2000.

The legislators argued that the Constitution reserves the power to draw district lines to state legislatures, not a commission created by initiative. That argument was rejected by the court’s four liberal justices plus Anthony Kennedy, a frequent swing voter.

“The invention of the initiative was in full harmony with the Constitution’s conception of the people as the font of governmental power,” Justice Ruth Bader Ginsburg wrote.

Led by Chief Justice John Roberts, the dissenters said the majority relied on “disconnected observations about direct democracy, a contorted interpretation of an irrelevant statute and naked appeals to public policy.”

The decision left the status quo intact for Arizona and 12 other states that have commissions with varying roles in drawing congressional lines.

Overall, Republicans have a 246-188 House majority, plus a vacancy in one GOP-leaning district.

Analysts attribute part of that advantage to Democrats’ concentration in dense urban areas. But it also reflects district lines Republicans drew after making major gains in 2010 state elections. In 2012, GOP House candidates got 1.4 million fewer votes than Democrats but won a 33-seat majority.

The GOP controls the governorship and legislature of 24 states, including Nebraska’s officially nonpartisan legislature. Seven states are run by Democrats and 19 are split, according to the National Conference of State Legislatures.