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An 8th Grade Class Tackles Gerrymandering

Jon Kimmel's class at Westtown School near Philadelphia used voter data to create new versions of a Pennsylvania congressional map.

As you have no doubt heard, Pennsylvania is at the center of the conversation about gerrymandering. Jon Kimmel decided that this conversation represented a teachable moment. So he used the state congressional map to teach his 8th graders about math and politics.

By Jon Kimmel
Mathematics and Art Teacher, Westttown School

After seeing a map of Pennsylvania’s 7th Congressional District this fall, my middle school math students asked how somebody came up with that shape.

The fact that many of us live in that district increased our interest. At this point the history of the Census, Congressional Redistricting, and Gerrymandering are becoming quite familiar to residents of states such as Pennsylvania, Wisconsin, North Carolina, and Maryland.

"We could do better"

My students, getting their first taste, were amazed at the audacity, flabbergasted at what this meant about Democracy, and more than a little amused at the stupidity of adults.

“We could do better than that!” said a kid in the back row. Let me tell you how my 8th graders did a better job than our illustrious legislature.

There are several publicly available Internet databases that link interactive maps with the voting precincts of Pennsylvania, their populations, and their vote totals for past elections. Together, my students agreed on several non-partisan approaches to grouping voting precincts into Congressional Districts, recognizing the accepted criteria for making districts: equal population, contiguous territory, and compactness.

While the current Pennsylvania maps meet the first criteria, they are contiguous in letter only, with districts such as the 7th barely more than a street wide in three separate spots, as it lurches over many counties seeking to include some voters while excluding others. The third standard, compactness, was visibly not considered in making this current map.

Circles, squares, and rectangles

As a math class, we tried to define compactness. While a circle is the most efficient shape as a ratio of perimeter to area, it is not a good shape to use in dividing up a state as it leaves many gaps. A rectangle, or even better a square, was my students’ solution.

So, one group made districts as much like squares as practical. Two other groups made maps as much like rectangular grids as possible. Another tried to follow county lines, on the theory those residents already had established common interests that transcend political party. One group just clicked randomly until they had enough people in each district. Others experimented with promoting competition (our only group to use voting records), and creating Multi-Member Districts.

In fewer than ten 43-minute classes, my students created eight different redistricting maps. They are not perfect. We concluded that there is no mathematically perfect way to do this, but there are ways that seem reasonable and ones that do not. And, pretty much anyone can tell the difference when looking at maps across a large room. The existing map plainly does not pass that test.

We suspected that looking compact and being compact were the same thing but wanted mathematical proof.  By measuring the area and perimeter of our districts and the existing ones, we could compare, say, the districts’ areas to that of a square with the same perimeter, and vice versa.

While the current legislature-created districts are about 45% as compact as a square, each of my students’ creations was closer to 70%, with some distinctly higher. Some of our lines are still less regular than we’d like, as we followed the existing irregular voter precinct lines.

Representation and the Efficiency Gap

Another consideration was whether the views of Pennsylvanians were reflected in their Congressional representation. In a state where Trump won by less than 1%, one would think that the U.S. Representatives would be evenly split, not the current 13-5 Republican majority.

The Efficiency Gap takes the difference between the wasted votes for each party and divides that by total voters. The “wasted votes” are all votes for a losing candidate plus all votes above those needed to win. Thinking about a Congressional District, such as PA-2nd, where 92% voted for Clinton, one can visualize wasted votes. The point is, that’s not an accident. But it is avoidable.

Political scientists argue that an Efficiency Gap over 7% is a likely sign of Gerrymandering, and unlikely to be overcome by elections over the ten-year life of the CD map. Pennsylvania’s Efficiency Gap is over 14%. The districts my students created, in contrast, had Efficiency Gaps around 3%, with several groups significantly lower.

If my 8th graders can draft Congressional District maps that are very representative and compact, why can’t the Pennsylvania Legislature? Obviously, the wrong people are in charge of the process.  If the goals of the mapmakers are non-partisan and the mapmakers themselves do not have a personal or partisan interest in the resulting maps, this is not a complicated or unfair process.

The mapmakers should have the goal of promoting democracy and equal representation for all Pennsylvanians. And if the state legislature cannot figure out how to represent its citizens, I know some great 14-year olds who already have.