Gerrymandering & Sampling Distributions
By Chris Olsen & Max Cembalest (guest contributors)
In 2019, a group of mathematicians wrote a brief to the Supreme Court that proposed an elegant and nonpartisan method for evaluating whether state districts were gerrymandered. It turns out, this method is also analogous to a concept at the heart of AP Stats: Sampling Distributions.
The method is called the simulation method. Here are the steps:
Have a computer draw a bunch of randomly simulated maps under two rules: a) districts have equal population sizes, b) no weird shapes.
Using prior election data, estimate how well Democrats and Republicans would do in each of the randomly drawn maps.
See if the map drawn by the actual state legislature is unusual (in terms of projected election outcomes) compared to the randomly simulated maps.
The distribution of simulated maps is akin to a sampling distribution. The legislature's map is akin to the measured statistic. Then, when you see how many simulated maps are more extreme than the legislature's map, you get a "p-value." And, just like a typical test, that p-value tells you whether you should reject the legislature's map!
To make this come alive for students, we built an applet where they can explore their own state (more states will be added as maps are approved). The accompanying lesson takes students through cases where both parties drew fair maps. Then, it takes students through cases where both parties, unfortunately, drew unfair maps.
Our hope is that the lesson helps students develop an intuitive foundation for sampling distributions and hypothesis tests. And, beyond that, we hope it inspires student awareness of nonpartisan redistricting reforms. Then, maybe one day, they'll help figure out bipartisan solutions so that all voices (regardless of background or party) can get fair representation in government.
Let’s skew it!