6 comments on “How can we measure the egregiousness of gerrymandering? Geometry, Perimeter, and Area”

How can we measure the egregiousness of gerrymandering? Geometry, Perimeter, and Area

Artifacts

This NY Times article/interview conducted by FiveThirtyEight.com’s Nate Silver and David Wasserman, House editor of the Cook Political Report. Particularly this snippet:

And/or this slideshow from Slate showing the most gerrymandered congressional districts in the nation.

Here’s my favorite from Illinois:

It’s worth noting that by federal law, congressional districts have to be “contiguous.” That means that (apparently) you can have a sidewalk connecting two blobs and you can call that contiguous.

Guiding Questions

  • What is gerrymandering?
  • Why do political parties do this?
  • Do the political parties that gerrymander egregiously like this ever get punished?
  • Is this really legal?
  • So, how can we measure “compactness”?
  • Would our measure of “compactness” yield the same top gerrymandered districts that Slate came up with?
  • What are the least gerrymandered districts in the U.S.?
  • How do we find the area of irregular shapes?

Suggested activities

  • Time to get you maps, compasses, colored pencils, and rulers out, just like Lewis and Clark.
  • Have students develop a metric or method to measure the “compactness” of a congressional district, particularly their own.
  • Students may want to research a history of gerrymandering, or the gerrymandering that has taken place in their state. I say, go for it. It might cross over into History and Political Science, but that’s definitely a good thing when it comes to HS and MS students.
  • The intended audience for such activities could range from politicians to political scientists to community board members. (aside: if you really want to rankle people in the community, I suggest looking at gerrymandering for school zones)
  • Assign each group a congressional district and ask them to develop a case for why theirs is the most egregious example of gerrymandering using geometry.

Potential solutions

  • While there isn’t necessarily one true, correct solution, it seems to me you could come up with a perimeter-to-area metric to measure the compactness, sort of analagous to the surface area-to-volume ratio that dictates how quickly, say, ice melts.
  • Or the centrality of or distance between the population centers. Perhaps analogous to the center of gravity, you can imagine if you were to cut out the shape of a congressional district and add mass by population and location, the more unstable it is, perhaps the less compact it is. (note: this is not necessarily true, but worth investigating)
  • Other potential metrics for students to measure: The distance between a population center and the borders of the distrct. Is there a way we could assign a penalty for districts who have conspicuous gaps or, as in the case in Illinois above, a tiny stretch of road (or something) connecting two large areas?
  • Ask each group to come up with a congressional district map for their state that is less gerrymandered than it currently is and demonstrate why mathematically. You could certainly envision a scenario in which an actual politician or political scientist may want to sit in on a panel. Certainly, your students can come up with a more mathematically appropriate map of congressional districts than this:


  • Note: as for the least gerrymandered congressional districts, that has to be a tie for first place between Wyoming, Montana, etc. because, well, you know….

How else could we measure the compactness and/or the egregiousness of gerrymandering?