Section 4.4 Big Problem: Using Mathematics to Determine Fairness
What is a “fair” district map?
Even without partisan bias, the notion of a “fair” district map may take on different meanings depending on your state and point of view. Perhaps a fair map is one that reliably produces representatives which are proportional to the state's political party populations. Maybe a map with a high number of competitive districts keeps democracy flourishing. Or possibly a state's geography prioritizes compactness of district shapes.
The good news is that mathematics provides tools to measure various forms of “fairness” in addition to ways to detect both forms of gerrymandering. We begin in Section 4.5 by introducing compactness formulas to quantify the geometry of districts. Then in Section 4.6, we use a couple of different mathematical approaches to investigate partisan gerrymandering. Next, in Section 4.7, we unpack the ways statistics can be used to unveil racial gerrymandering. Finally, in Section 4.8 we introduce the concept of outlier analysis as a way to identify unfair maps.