Gerrymandering is a hot topic in certain circles.
Right now I am in the midst of writing and modifying some gerrymandering activities for my summer course at Crimson Summer Academy (CSA). Although we have taught various voting methods since the beginning of CSA almost 20 years ago, we had never included gerrymandering as a topic within our applied math course, Quantitative Reasoning (QR). That avoidance has to stop!
Let’s look at one example of gerrymandering: Pennsylvania’s 7th Congressional district. Here is a set of pictures of the shape of the district as it evolved from 1952 to 2013:
Districts in general are supposed to be closed, compact, and roughly equal in population. Even without population data, it’s still intuitively clear that the districts in 1972 and 2002 are pretty suspect and that the one in 2013 is wildly inappropriate to the point that it boggles the mind. But how to quantify this problem so that a court could create a legal rule? It seems to have something to do with area and perimeter, doesn’t it? Hence the decision to include it in an applied math course. (It could also be in a civics course, but they don’t seem to exist anymore.)
Gerrymandering is both mathematically and politically important, as states have been known to use it to implement such heinous acts as putting almost all people of color in a single district (“packing”) so that they can’t elect more than one person of color as a representative, or splitting almost all people of color among four different districts (“cracking”) so they can’t form a majority in any single district. It doesn’t have to be racial; it can also be by political party, which the Supreme Court doesn’t seem to object to.
Anyway, we’ve been writing some gerrymandering problems at CSA, based on prior work by teachers at Weston High School, Tufts University, and elsewhere. So stay tuned.