Discrete geometry for electoral geography

Understand

"Compactness," or the use of shape as a proxy for fairness, has been a long-running theme in the scrutiny of electoral districts; badly-shaped districts are often flagged as examples of the abuse of power known as gerrymandering.

• The most popular compactness metrics in the redistricting literature belong to a class of scores that we call contour-based, making heavy use of area and perimeter.
• This entire class of district scores has some common drawbacks, outlined here.
• We make the case for discrete shape scores and offer two promising ideas: a cut score and a spanning tree score.