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


This NY Times article/interview conducted by’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?

This entry was posted in area, civis, geometry, perimeter, tasks. Bookmark the permalink.

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

  1. MrHonner says:

    What a great idea! A clear, direct, and compelling application of substantial mathematical ideas to a seemingly non-mathematical problem. Easy to see a group of students conducting a study and then presenting their findings to local governments and politicians. Well done, Geoff.

    I particularly love the center-of-mass extension. Look at population densities, maybe even bring some calculus to the fold.

  2. Pingback: “Isn’t Problem Based Learning easier than Project Based Learning?” and 10 other myths about PrBL, (“Real or not real”) | emergent math

  3. Pingback: Consider Magazine » Blog Archive » Gerrymeanderings

  4. I know this is an old post, but it is exactly what I was looking for! I’m focusing on voting and apportionment for my probability unit because gerrymandering is more interesting than random number generators & the like. We’re starting next week – thanks for the guiding questions, those will be really helpful.

    • Geoff says:

      That’s great! Let me know how it does and what you guys end up doing with it!

      • It went pretty well for the first time doing it! I gave each group of 3-4 a state with 4 districts, then had them compare how many representatives were elected from each party vs. proportionally how many should have been based on presidential elections. Then I gave them the county-by-county electoral map, demographic information about each district, and asked them to identify examples of gerrymandering, backing it up with statistics. Then I asked them to re-district, but without knowing the population of every single county this was a super tall task. I’m also using a ton of activities from Is Democracy Fair?, this book from 1997. That is a pretty great book.

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