Gill v. Whitford and the Math of Gerrymandering

On October 3, 2017, the Supreme Court heard oral arguments in Gill v. Whitford, 137 S. Ct. 2268 (Mem) (2017), the latest case to reach the court contesting partisan gerrymandering. First coined in 1812 to lampoon a Massachusetts governor (Elbridge Gerry) and a particularly ugly congressional district (allegedly resembling a salamander), gerrymandering is the practice of crafting voting districts to give one group an electoral advantage over another. Erica Klarre, Gerrymandering Is Illegal, But Only Mathematicians Can Prove It, WIRED (April 16, 2017), The basic strategy is to “pack” a large number of your opponents into a small number of districts where they win in a landslide, while “cracking” a small number of your opponents across a large number of districts where they narrowly lose. This maximizes your electoral victories, while minimizing those of your opponents. Though these districts may offend the eye (See Jennifer Davis, Elbridge Gerry and the Monstrous Gerrymander, IN CUSTODIA LEGIS, LAW LIBRARIANS OF CONGRESS (February 10, 2017),, unless they violate the Voting Rights Act or the Equal Protection Clause of the 14th amendment, whose provisions have typically been held to only apply to protected classes such as race, they are not illegal. The issue raised in Gill is whether gerrymandered districts created for partisan political purposes violate the Equal Protection clause of the 14th amendment, Whitford v. Gill, 218 F. Supp. 3d 837, 928 (W.D. Wis. 2016). This obviously raises legal issues that have the potential to shape electoral politics across the nation, but the gerrymandered districts owe their creation, and perhaps their undoing, not to law, but to math.

The districts at issue in Gill are Wisconsin’s congressional districts drawn after the 2010 census. Id. at 843. In 2011, Wisconsin’s Republican controlled state legislature redrew the state’s electoral districts. The districts were drawn with the aid of a computer modeling tool developed by University of Oklahoma political science Professor Keith Gaddie. Emily Bazelon, The New Front in the Gerrymandering Wars: Democracy vs. Math, THE NEW YORK TIMES MAGAZINE (August 29, 2017), Gaddie’s tool measured the partisanship of precincts across Wisconsin. Republicans used that data to draw possible electoral maps. Gaddie’s tool then compared how different electoral district maps would lead to different potential electoral outcomes to identify which arrangement of electoral districts would maximize Republican victories. In each of the elections after the redistricting plan went into place, Republicans gained seats in the Wisconsin legislature. Democratic voters brought suit to challenge the redistricting plan, arguing that the Republican electoral victories were a result of the partisan dilution of Democratic voters in Wisconsin’s electoral districts in violation the Equal Protection Clause of the 14th Amendment and the rights of association and free speech guaranteed in the First Amendment. Whitford, 218 F. Supp. 3d at 843.

In 2016, the Federal District Court for the Western District of Wisconsin ruled in the Democrats’ favor, holding that the plan intentionally burdened the representation of Democratic voters and that the plan constituted an unconstitutional political gerrymander. Id. The Supreme Court has made the claim that excess injection of politics into gerrymandering is unlawful, but have not made clear what constitutes “excessive injection,” and has not previously struck down a redistricting plan for partisanship. Vieth v. Jubelirer, 541 U.S. 267, 293 (2004). The plaintiffs in Whitford made their excessiveness claim using the circumstances surrounding the redistricting, but also used math to fight math. The plaintiffs’ main argument for the excessiveness of the political gerrymander lay in a way of interpreting the asymmetry of election results called “the efficiency gap.” Whitford 218 F.Supp.3d at 898. The efficiency gap measures so-called “wasted votes,” which include packed votes, votes cast over the 50% line for a winner in a district, and cracked votes, the number of votes cast for a losing candidate. The wasted votes of the parties are compared to give a percentage of advantage. Essentially, lower efficiency gaps result in more fair elections, while larger efficiency gaps, result in less fair elections. The plaintiffs showed that the redistricting plan resulted in an average efficiency gap for the Republicans of 9.5% over the life of the plan, above the level needed to secure their legislative control (7%). Whitford 218 F.Supp.3d at 905-06.

The case argued before the Supreme Court earlier this month, Gill, has more statistical evidence to bolster the Democrats’ claims. In addition to the efficiency gap described above, the plaintiffs used computers to draw maps of their own. By drawing a large number of random plausible maps, they compared the efficiency gaps of the Republican map to the random maps. Jowei Chen, The Impact of Political Geography on Wisconsin Redistricting: An Analysis of Wisconsin’s Act 43 Assembly Districting Plan, 16 ELECTION L. J. 1 (2017). The results showed that a large number of possible maps could have been drawn with much lower efficiency gaps, thus casting doubt on the Republican plan as anything but a partisan gerrymander. Jordan Ellenberg, How Computers Turned Gerrymandering Into a Science, THE NEW YORK TIMES (October 6, 2017),

The computational arguments advanced by the plaintiffs are novel, and, at least in the district court, persuasive. We await the results of these arguments from the Supreme Court, but if they do strike down the redistricting plan, the decision will have major repercussions for voting rights and redistricting. It will also be a major victory for computation and statistical evidence in the court room, perhaps opening doors to novel solutions to old problems across the legal sphere.

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