How to Measure Gerrymandering

Specific equations have been found to detect instances of gerrymandering in real world political districts. These equations are used to measure a district's compactness. Compactness is something that has many different definitions. The Gerrymandering equations below are different ways that we use to measure different types of compactness in districts, in order to detect in what ways a district may be gerrymandered. A non-gerrymandered district would have high scores on all of the measurements below.

Harris:

W/L, where L is the district's longest dimension, and W is the width perpendicular to that axis. This measure is a shape is long and skinny, and therefor not compact, or is shaped like a square or circle, and not gerrymandered.

Polsby-Popper:

4πA/p^2, where A is the district's area and P is the district's perimeter. A compact district or figure will have as much area as possible within as little perimeter as possible. A district with a large perimeter and small area is not compact, and is gerrymandered.

Reock:

A/C, where A is the district's area and C is the area of the smallest circle containing the district. This measures how close the district's area is to a circle, the most compact shape. The closer a district is to a circle the less gerrymandered it is.

Convex Hull Measure:

A/H, where A is the district's area and H is the area of its convex hull. A convex shape is a shape where any straight line that runs through the shape will only cross the perimeter twice, once to enter the figure, and once to exit the figure. When a shape is convex, the area is typically closer together than the area in a concave shape. This measures how compact the figure is based off whether it is concave or not. According to this equation a more concave shape is a less gerrymandered district.