Richard Barnes writes:

In this article (preprint here) we explore a similar concept to forking paths applied to quantifying electoral gerrymandering.

(Some) efforts to quantify electoral gerrymandering aim to come up with a mathematical measure of how “oddly” a district is shaped. In the paper, we show that in translating from real-world geography to math-world a number of choices need to be made which collectively make a kind of garden: the compounding effects of the choices can make the mathematical measure of gerrymandering take almost any value.

An unwary researcher might simply accept their final quantification of gerrymandering without realizing it’s just one of many possibilities while a bad actor could actively manipulate the choices to achieve a desired outcome.

The image above visualizes this. Different mappings from real-world data to math-world are applied to every electoral district in the US (grey distribution) while the district in question is shown with a black line. There’s quite a difference between the best and worst representations.

Perhaps the most general take-away is that doing mathematics that involves real-world geography can be a risky endeavour!