How It Works

We explore two ideas here:

• The most population compact map is the natural starting point for redistricting — all redistricting plans for a state are informed by it; and

• Comparing redistricting plans to that starting point highlights the mix of policy choices (trade-offs) that the mapmakers made.

By population geography we mean how many people live where in a state.

From here on, bolded terms are defined on the Glossary page.

In more detail:

1. We introduce the concept of a root plan or root map that partitions a state’s unique population geography into a set of districts with the lowest overall edit distance to all other valid maps. Due to computational limitations, one can only approximate the root map.

2. We argue that maximally population compact districts are the natural starting point for redistricting.

   The fundamental principle of these maps is that people who live near each other will tend to be in the same district. Moreover, they are a good heuristic for approximating root maps.

   Maps that are highly compact geometrically also tend to have low overall edit distances to other valid maps — slightly lower than population compact maps. But as Chief Justice Earl Warren said in his landmark Reynold v. Sims decision, “Legislators represent people, not trees or acres.” so the heuristic we use to approximate root maps is to maximize population compactness.

   Roughly speaking, population-compact districts form a Voronoi diagram.

   We impose three additional constraints on our approximation:

   • Each district is contiguous
   • No precincts are split, and
   • Population deviation is 2% or less

   From an initial, random districting, our algorithm greedily searches for the most population-compact districting. Because this algorithm is not guaranteed to find the best districting, we run it 100 times and take the best qualifying map.

3. We also believe it is logical to think of other maps in terms of deltas from these root maps. A root map isn’t a priori (or independently) normative though. Think of it like the origin on a set of axes: it’s simply the place from which you describe other points.

4. We generate proximal root maps for 42 states apportioned two or more congressional districts in the 2020 census. We exclude Hawaii and Maine, due to data issues.

5. We compare these root maps to the five notable maps from Dave’s Redistricting (DRA) for each state that individually optimize for proportionality, competitiveness, minority representation, compactness, and county-district splitting.

6. Despite optimizing on these different dimensions, these maps share substantial common core districts with the root map, an average of nearly two thirds of the population-weighted assignments (65.9%). This reinforces our hypothesis that maximizing the overall population compactness of districts is a good way to characterize population geography.

7. Then we compare the DRA ratings for these divergent maps to those for the root map showing some major quantifiable policy trade-offs inherent in congressional redistricting for each state. These contrasts put policy choices framed by the underlying population geography in sharp relief.

   Again, these root maps are not normative — they aren’t what we think redistricting plans should be. Given their very low overall edit distance to other valid maps, all redistricting plans for a state are unavoidably informed by them, and they are easy to understand conceptually — people who live near each other will tend to be in the same district.

   Hence, they provide a good baseline against which to evaluate and compare plans.

8. Finally, we compare the official map for each state to the root districts showing the mix of policy choices (trade-offs) that each state made.

For more background, see the Background page.