A dispute over Wisconsin’s Republican-drawn boundaries for the state legislature offers Democrats some hope of cutting into GOP electoral majorities across the United States. Election law experts say the case is the best chance yet for the high court to put limits on what lawmakers may do to gain a partisan advantage in creating political district maps.

The justices could say as early as Monday whether they will intervene.

The Constitution requires states to redo their political maps to reflect population changes identified in the once-a-decade census. The issue of gerrymandering — creating districts that often are oddly shaped and with the aim of benefiting one party — is centuries old. The term comes from a Massachusetts state Senate district that resembled a salamander and was approved in 1812 by Massachusetts Gov. Elbridge Gerry.

Both parties have sought the largest partisan edge when they control redistricting. Yet Democrats are more supportive of having courts rein in extreme districting plans, mainly because Republicans control more legislatures and drew districts after the 2010 census that enhanced their advantage in those states and in the U.S. House of Representatives.

In the Wisconsin case, a federal court struck down the districts as unconstitutional in November, finding they were drawn to unfairly minimize the influence of Democratic voters.

The challengers to the Wisconsin districts say it is an extreme example of redistricting that has led to ever-increasing polarization in American politics because so few districts are genuinely competitive between the parties. In these safe seats, incumbents tend to be more concerned about primary challengers, so they try to appeal mostly to their party’s base.

“If the court is not willing to draw a line here, it would suggest the court is unlikely ever to feel comfortable setting a limit,” said Richard Pildes, an election law expert at New York University’s law school.

Defenders of the Wisconsin plan argue that the election results it produced are similar to those under earlier court-drawn maps. They say the federal court overstepped its bounds and judges should stay out of an inherently political exercise.

The justices should correct the lower court’s “flawed analysis before it spreads to other jurisdictions and interferes with the states’ fundamental political responsibilities,” Texas Solicitor General Scott Keller wrote for 12 Republican-dominated states that are backing Wisconsin.

The issue has torn the court for decades. Some justices believe courts have no role to play in a matter best left to elected officials. Others say courts should step in. In 2004, Justice Anthony Kennedy staked out a position somewhere between those two views, saying courts could referee claims of excessively partisan redistricting, but only if they can find a workable way to do so. In that case and again in 2006, Kennedy didn’t find one.

The Supreme Court has never struck down districts because of unfair partisan advantage, although it has intervened frequently in disputes over race and redistricting over the past 50 years.

Similar lawsuits are pending in Maryland, where Democrats dominate, and North Carolina, where Republicans have a huge edge in the congressional delegation and the state legislature.

“The court is surely aware that this decade produced some of the most aggressive partisan gerrymandering in the modern era,” Pildes said.

The Wisconsin case seems promising because the lower court said it found a way to measure the partisan nature of the districts. The court adopted an equation offered by the challengers that essentially measures and compares each party’s wasted votes —those going to the winner in excess of what’s needed for victory — in an election. Republicans might stuff Democratic voters into Democratic districts, leaving other districts with Republican majorities that are essentially just large enough to elect GOP candidates.

This “efficiency gap” identifies districting plans that are likely to accentuate one party’s control over the 10-year life of the plans, said Eric McGhee, a research fellow at the Public Policy Institute of California who helped develop the measurement.

Wisconsin Republicans drew the maps in 2011 after they took full control of state government in the 2010 elections. Under those maps in 2012, Republicans captured 61 percent of state assembly seats while winning 48.6 percent of the statewide vote. They now have their largest majorities in the state House and Senate in decades.

Republicans argue they are successful because they run better candidates in a state that is trending Republican. They also say they have a natural edge in redistricting, since Democrats tend to cluster in cities and suburbs, creating districts that overwhelmingly vote Democratic.