Think of the partitioned rectangle below as a simple map. Each square represents the home of a single voter. Each voter is a member of one of two parties, the red party or the blue party. There are
- 30 blue voters and
- 20 red voters.
The objective is to partition these voters into 5 districts of 10 voters each. Each district should be formed by merging 10 squares along adjacent edges and should form one contiguous piece. The map is interactive so that you can select the squares by clicking on them. See if you can create sets of districts that satisfy each of the following criteria:
- The districts fairly represent the overall population
- All districts are predominantly blue
- Most districts are predominantly red
- The districts are fair and competitive.
- The number of ties is maximized.
Another desirable criterion is compactness. Intuitively, this means that the districts aren’t to stretched out, which is often a sign of intentional gerrymandering. Quantitatively, we can define the compactness score of a district as the ratio of its perimeter to its area. In each of the above scenarios, you might consider if the compactness can be improved.
Clearly, this is highly idealized and overly simplified, even for a map of a region in a highly regimented town in the great plains. The objective, though, is to understand the very basics of gerrymandering and, often, the best way to learn something is to try it yourself. Thus, it makes sense to start with a really simple example.
The map is not my invention. As far as I know, this particular map first appeared in this Washington Post article but it’s appeared on many blogs, posts, and web pages since, including Wikipedia’s Gerrymandering article.
- The districts fairly represent the overall population
- All districts are predominantly blue
- Most districts are predominantly red
- The districts are fair and competitive.
Solutions
I’ve built some solutions to the challenges using the interactive map above. You can view them by checking the “Show solutions” box. These solutions are far from unique; there are certainly many more.