The Gerrymander: A Thriving Species

By Henryka Maslowski

A mathematician looks at the gerrymander, its techniques and its prospects.

What species should be endangered but is not? Although seven out of ten Americans would be happy to see it go extinct, it may have protection in high places. And if all else fails, it is capable of evolving.

The species, of course, is the gerrymander, that parasitical creature that came into existence at the same time as voting districts, that nibbles away at democracy and tries to foil the will of the people. As is well-known, the gerrymander was identified in 1812 by political cartoonist Elkanah Tisdale, who recognized it in a map of voting districts for the state legislature in Massachusetts where Elbridge Gerry was running for a second term as governor. “Gerrymandering” is the name given to the practice of drawing the boundaries of voting districts in order to maximize the electoral success of whoever is responsible for drawing districts. Traditionally such districts could be recognized by a weird shape that hints at some scheming behind the districting process. We will see that that is no longer the case: A gerrymander can be genetically engineered to look like a hedgehog.

There are standard techniques that gerrymanders use to do their dirty work for the party in charge of drawing districts. “Cracking” involves dispersing voters of the opposing party over several districts to prevent them from achieving a majority anywhere. “Packing”, in some ways the opposite of cracking, combines as many as possible voters from the opposing party into as few as possible districts to prevent them from affecting outcomes in other districts. Packing is useful if the opposing party has an overall majority in a state and thus its influence cannot be completely diluted. “Stacking” is especially insidious. Here, a district is formed to include people of high income/high education and also those of low income/low education. The idea is that the latter are unlikely to vote so that those drawing the boundary can boast of inclusiveness and at the same time know that the district is, in fact, a gerrymander. All these techniques assume knowledge of locations and concentrations of voters of both parties.

The US Constitution says nowhere that there must be congressional districts. It only specifies that “the House of Representatives shall be composed of members chosen every second year by the several states.” Not until after the Civil War did congressional districts become the norm.

The Supreme Court emphatically declares that gerrymandering for racial advantage is unconstitutional, but it has avoided making a ruling on partisan gerrymanders. Justice Kennedy, in 2004, held out the possibility that he would support a challenge in gerrymandering cases if “a workable standard” could be found to decide whether a district had been gerrymandered.

Mathematicians are hard at work to develop such a standard. A group at the University of Michigan under Jowei Chen has been running computer simulations of possible districts and comparing their outcomes with the actual election results. At Tufts University, Moon Duchin leads a research group on “Metric Geometry and Gerrymandering.”

There is a clever mathematical argument showing that, given a roughly convex shaped region (a state) with a known distribution of voters from parties A and B, there must exist a line that divides the region into two subregions, both roughly convex, so that on either side of the line you find half the voters of party A and half the voters of party B. Thus the two subregions preserve the same ratio of A and B voters as the original region. Repetition of this construction, say, three more times gives 16 districts where a party with only a slight majority can win all 16 districts. Our gerrymander now mimics the shape of a cute, roly poly hedgehog.

Computer simulations and probability arguments can help in identifying gerrymanders. The idea seems simple on the surface: If an outcome occurs that has an extremely low probability (such as 100 heads in 100 tosses of a coin) and if the probabilities can be easily calculated using high speed computers, we should be able to spot rigged outcomes. There are caveats: dealing with probabilities can be slippery. Our confidence in the result is itself measured by a probability. Low probability events can occur. Computer simulations suggest that actual voting districts have given the party in charge of districting (usually Republican) more, but not significantly more, votes than most of the simulated plans would have. Chen thinks this is because Democrats are more likely to be concentrated in cities and college towns, while Republicans are fairly evenly distributed outside of cities, as if by a natural gerrymander.

Something called the “efficiency gap” has been getting attention lately as a possible measure of the extent of gerrymandering. It has some problems, (too technical to describe here) but can be useful when combined with other measures. To start with, the efficiency gap is built on the idea of “wasted votes,” a concept that seems to me to be problematic for democracy. A vote is considered “wasted” if 1) it is cast for a losing candidate or 2) it is cast for a winning candidate who already has enough votes to win. For example, candidate A needs 51 votes to win. The 52nd, 53rd, etc. votes are “wasted.” Calling some votes “wasted” underscores the horse-race aspect of elections, is demoralizing for democracy, erases the difference between a narrow win and a landslide, and it discourages voter turnout in elections where one of the candidates is the presumed winner. The efficiency gap cannot be calculated for a single district, but must include all the districts in a state. It adds up the “wasted” votes, over all districts, for each party separately and then divides the difference by the total turnout for the election. A large positive or negative value would show that one party has ”wasted” disproportionately more votes, indicating gerrymandering. This is the measure that Justice John Roberts called “sociological gobbledygook.” “The intelligent man on the street is going to say that’s a bunch of baloney.” (If the concept is too complicated for our chief justice, he can easily call on qualified people to explain it to him.) Judge James A. Wynn, Jr, of the US Court of Appeals has the perfect reply: ‘The Constitution does not require federal courts to act like Galileo’s Inquisition and enjoin consideration of new academic theories.”

Elbridge Gerry was himself a (proto) Democrat, and Democrats have in the past been guilty of gerrymandering. Today, however, Republicans, being in the ascendancy in most states, are more culpable of the practice. What is disturbing is that they have become shameless about it. Here is what some prominent Republicans say:

Mitch McConnell: “...the left effort to outlaw gerrymandering” “What do you think the founding fathers had in mind?...They thought it was going to be a political exercise.”

Justice Alito: “Hasn’t this court said time and again that you can’t take all consideration of partisan advantage out of districting? ...Were the Supreme Court to forbid taking account of politics in drawing voting maps, I really don’t see how we will ever be able to district.”

North Carolina state senator Mark McDaniel: “We are in the business of rigging elections.” David Lewis (another NC state senator). “I think electing Republicans is better than electing Democrats, so I drew the map to help foster what I think is better for our country.”

The gerrymander doesn’t need a change in shape or protective coloring to survive.