One obstacle is that the Supreme Court has yet to recognize a discernible and manageable standard for identifying unconstitutional partisan gerrymanders. In our recent book, “Gerrymandering in America,” we show that there is indeed a standard to judge these cases that can be directly derived from the Constitution.

Partisan gerrymandering has gotten out of control

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Partisan gerrymandering has always been with us. After the Supreme Court decisions of the 1960s, however, the level of partisan bias was minor.

This changed in the round of redistricting following the 2010 U.S. Census. By our calculations, partisan bias in congressional district maps tripled compared to the post-2000 districts — and in a way that gave a big advantage to the Republican Party. To win back the U.S. House of Representatives, the Democrats would need to win between 54 and 55 percent of the popular vote — a level similar to 2008, when both economic and political conditions greatly favored the Democratic Party.

This increase in partisan bias followed the Supreme Court’s 2004 decision in Vieth v Jubelirer, which established that there was no standard for adjudicating cases of partisan gerrymandering. Justice Antonin Scalia, joined by three other justices, argued that gerrymandering for partisan gain was inherently “non-justiciable” — it was a political matter in which the court had no business intervening.

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As a result, state governments did not have to fear judicial reprimand, and so were free to push partisan gerrymandering to the limit. But with the death of Scalia and the recent successful challenge to Wisconsin’s state legislative maps, this 5-4 ruling appears increasingly vulnerable. Although Justice Anthony M. Kennedy agreed in Vieth that no single standard currently existed, he held out the possibility that one could be identified.

The challenge for reformers, however, is that the courts need a judicial standard, which is different from a mere scientific standard. A judicial standard must be judicially discernible — it has to be derived from a specific right given in the Constitution. It also has to be judicially manageable — it needs to provide courts with clear guidance on how to rule.

There is a perfectly good scientific standard for determining whether there is partisan gerrymandering. This is the “partisan symmetry” measure developed by Andrew Gelman and Gary King. Essentially, symmetry requires that a specific share of the popular vote (say, 60 percent) would translate into the same number of congressional seats, regardless of which party won that share of the vote. For instance, if winning 60 percent of the popular vote in a state gives the Republican Party 65 percent of the congressional seats, then the Democratic Party should also win 65 percent of the seats if it wins 60 percent of the vote.

Notably, this is not as strict as a proportionality standard, which would require that each party’s voters obtain a share of seats in proportion to the party’s vote share. Symmetry simply demands that every voter receives the same strength of representation, regardless of which party they vote for. There are proven, well-established techniques to measure symmetry and provide error bounds.

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The main difficulty is showing that this scientific standard is judicially discernible. The partisan symmetry measure demonstrates where the two parties are not treated equally. But as Justice Scalia pointed out in his Vieth opinion, parties do not have a right to equal representation, any more than any other social group. It is only individual voters who have a right to equal treatment under the 14th Amendment and Article 1 of the Constitution.

In our book, we show that the partisan symmetry standard can be logically derived from the equal treatment of individual voters, based on recent results in social choice theory. In partisan elections, you cannot treat all individual voters equally without treating all parties equally. This means that the party that gets more votes must get more seats. This sounds obvious, but it is precisely what the Supreme Court did not accept in the Vieth case. We show — line by mathematical line — that this logic is inescapable.

If the party that gets the most votes nationally is to get a majority of the seats, then state districting plans also have to treat parties equally — that is, satisfy partisan symmetry. If a redistricting plan violates partisan symmetry, then it necessarily violates the equal treatment of individual voters. Thus, the partisan symmetry standard is indeed judicially discernible from the Constitution.

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The fact that partisan symmetry can be derived directly from equal protection is an important advantage over other standards that have been proposed (such as Nicholas Stephanopoulos and Eric McGhee’s “efficiency gap”). Such standards require additional assumptions that would need to be constitutionally justified.

Given that partisan symmetry is judicially discernible, it is straightforward to demonstrate that it is judicially manageable — that is, it gives clear guidance. We show that the congressional district maps in a majority of states very clearly do not violate the standard. It turns out that partisan symmetry is only a problem in states where one party controls the entire redistricting process. Eighteen states violate the standard, and only one of these (Indiana) is remotely close to meeting it.

Thus, we have a clear standard for measuring partisan gerrymandering that can be logically derived from the Constitution. This is a matter that the new Supreme Court may take up soon, and will have the opportunity to address. If they do not, the composition of the House of Representatives will continue to be determined by state legislatures once every 10 years, instead of by the people every two years.

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Anthony McGann is a professor at the School of Government and Public Policy in at the University of Strathclyde.

Charles Anthony Smith is a professor in the political science department at the University of California, Irvine.

Michael Latner is associate professor of political science at California Polytechnic State University. Find him on Twitter @mlatner.