The Problem Of Defining Gerrymandering

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In the 2012 Pennsylvania statehouse elections, 51% of the vote went to Democrats, but they received only 28% of the representatives. This wasn’t a fluke — in 6 other states Democrats received a minority fraction of state representatives while obtaining a majority of the votes, a pattern mirrored in federal elections. These results, declared a “shellacking” by President Obama, gave us a Republican majority in the House, created an entrenched Freedom Caucus, and produced several other equally-grim side-effects.

The origins of this strange mathematical phenomenon appear two years prior, in a gust of what is now seen to have been some incredibly effective political spending. Under the banner of REDMAP, Republicans pumped the relatively small sum of $30 million into targeted local races, taking control of several state legislatures. This granted them the power to redraw some congressional and state district maps after the census, which they quickly took advantage of.

Seeking district maps that benefitted them, mapmakers employed tactics like “packing” Democrats into small numbers of districts or “cracking” dense populations of Democrats (usually in cities) into multiple, sprawling districts where their votes were diluted by rural Republican voters. Access to unprecedented amounts of voter data and powerful predictive algorithms made this easy, and resulted in maps that served their makers extremely well

Drawing congressional districts that end up favoring a political party or candidate is called partisan gerrymandering, and is, in fact, illegal. How was this allowed to happen, then, with Republican operatives like Karl Rove brazenly declaring, “He who controls redistricting can control Congress”?

Legal Background and Current Case

The answer comes from the Supreme Court. Over 30 years ago in Davis v. Bandemer, they declared “extreme” partisan gerrymandering unconstitutional, but failed to establish a standard for use in determining if it was happening at all. Lower courts have searched for such a standard ever since, but the Supreme Court has yet to accept any of them.

The plaintiffs in the current Supreme Court case, Gill v. Whitford, hope to change this. If the court rules in their favor, lower courts will be freed from their current paralysis, allowing for successful legal challenges to gerrymandered maps.

Gill reviews a decision to invalidate the Wisconsin state legislature map for illegally favoring Republicans, who won around 60% of the state assembly seats with only 49% of the votes in 2012. The skew seems obvious, so why is there any controversy around this case? 

While the outcome of the election feels very wrong, proportional party representation is not a legal requirement for district maps. The law requires instead that plaintiffs show an asymmetrical, persistent bias against a particular political party. A lack of an agreed-upon method for showing this has been the biggest barrier in establishing a gerrymandering standard.

This is why the Gill plaintiffs engaged in a more complicated analysis in their claim. They rely on a computed quantity (or “metric”) called the “Efficiency Gap” (EG), meant to measure the number of “wasted votes” cast for a given political party. 

Their argument is based on the idea that the EG of the current map against the Democrats is unreasonably, persistently large and as a result, the votes of Democrats in Wisconsin were disproportionately wasted. 

If the court rejects this argument, the Wisconsin map will stand. There will continue to be no legal apparatus to challenge current gerrymanders or to prevent more egregious ones being drawn after the 2020 census — and, to be clear, they will be more egregious. 

Republicans are already teeing up REDMAP 2020, expecting to spend at least $125 million to push for further gerrymandering. The Democrats plan to launch their own PAC to counter the Republicans, an effort that could easily fail. The likely outcome of this will be, in the words of the Gill plaintiffs, “a festival of copycat gerrymandering the likes of which this country has never seen.”

What If SCOTUS Rules Against Wisconsin?

Even if such an apocalyptic scenario is averted by an invalidation of the Wisconsin map, partisan gerrymandering isn’t necessarily dead.

Court cases could be lost

A decision for the plaintiffs would simply leave room for gerrymandering cases to be decided in court, which could result in several problems, the first being that these cases will be messy. 

In court, those that defend gerrymandered maps will have the opportunity to intentionally misrepresent or misunderstand the arguments presented to show that gerrymandering has occurred. In addition, the technical nature of these arguments means that there might be confusion in the debate around them, undermining  the ability of well-meaning judges to arrive at correct conclusions. The history of racial gerrymandering cases tells us that this is a dangerous possibility and, moreover, both have already happened in Gill. 

If this happens with a relatively simple metric like the EG, it is bound to happen with more sophisticated  tests that will arise in the future, and doesn’t bode well for our ability to quickly strike down gerrymandered maps. 

Unintended consequences

Even if these court battles work out in our collective favor, congressional maps must still be drawn, and the legal standards set in gerrymandering cases could influence this process. 

By latching on too hard to metrics like the EG in calling out gerrymandering, minimizing them might be taken as a goal, and in doing so we risk incorporating the political biases of those metrics into new maps.

Some of the biases of the EG are revealed with simple algebra, indicating that its use can:

  • discourage proportional party allocation of representatives;
  • encourage uncompetitive districts;
  • be unpredictable in competitive races;
  • fail to allow for any maps that aren’t considered gerrymandered;
  • force drawing of bizarrely shaped districts.

It could get worse: the use of more sophisticated computational techniques and statistical methods will introduce biases that their users may not know of. Recent usages of machine learning techniques provide awful examples, and there is not a known way of avoiding this.

As a result, we could end up accidentally drawing maps with completely undesirable, unpredicted political properties.

An arms race

The final problem is technological: our tools to fight gerrymandering might not be good enough. 

Much like online spammers trying to outsmart email filters, perpetrators of gerrymandering will constantly engage in developing more advanced ways to undermine any court-established gerrymandering tests. 

With relative ease, a mapmaker can tell a computer, “Draw a legally-acceptable map that maximizes the number of seats that the Republicans are going to pick up while still having an EG less than 7%.”

Electoral polarization and the mountains of micro-targeted demographic and political data available to data scientists may make this a feasible problem to solve, producing gerrymandered maps that, from the perspective of the courts, don’t look it. 

Because intent is not enough to invalidate a map, this is completely legal. Maps can be implemented that were constructed with the explicit goal of fooling whatever test is being used at the moment — provided that they have succeeded in doing so. Those on the other side will be forced to improve their own anti-gerrymandering techniques to keep up in court, and they might not succeed. 

Jordan Ellenberg, a mathematician involved in gerrymandering research, describes the arms race this sets up succinctly:

You can use [advanced computation] to make electoral mischief, but you can also use it to detect and measure that mischief. It’s not math versus democracy; it’s math versus math, with democracy at stake.

On one side of this battle are academics, lawyers and others working to develop better methods for defining and detecting gerrymandering. On the other side are political operatives with vast private data and cynical political motivations.

One of these sides has access to far more resources than the other, and it’s not the one that we’d want to win.


All of the above suggests that contending with the existence of gerrymandered maps will be difficult. We’d be better off stopping them from being drawn in the first place.

Luckily, there are a variety of popular, relatively-mild political options to do so at our disposal, the most effective of which would be requiring transparent, independent commissions to draw district maps.

If done correctly, this would eliminate the structural problem of legislators being in a position of power to draw the district maps that they stand to benefit from. Six states already have already done so, and the resulting maps seem to produce more competitive congressional races. 

There are also more radical, better alternatives worth considering. Changing the voting system to one that provides proportional representation would end gerrymandering, and some proposals eliminate district maps entirely, getting rid of racial gerrymandering, partisan gerrymandering, and potential bias in one fell swoop. 

No matter what, it’s imperative that we implement some reforms to curb gerrymandering —  if we don’t, we’ll be permanently left with rigged maps, an unresponsive legislature, and a thoroughly-broken democracy.