Background

This page explains what we did and why we did it.

Contents

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

Motivation

The notable maps in Dave's Redistricting (DRA) are the maps that individually maximize five quantifiable policy dimensions: proportionality, competitiveness, opportunity for minority representation, compactness, and county-district splitting. For the 2020 congressional redistricting cycle, these maps demonstrated that there were tradeoffs between these objectives. For example, compact districts aren’t always fair, and vice versa.1

This led to the two hypotheses that motivated this research:

  1. In contrast to the notable and official maps that use a broad spectrum of data, our first hypothesis was that there are well-defined root districts for a state that only depend on total population — While Alec had introduced the concept several years ago as “baseline districts,”2 he had not written code to generate them automatically.

  2. Our second hypothesis was that the districts for the notable maps for a state overlap significantly. It seems obvious that — barring extremely serpentine districts — valid redistricting maps for a state must share common core areas because of the underlying population geography for a state, i.e., how many people live where. This is precisely what is characterized by our root districts. We wanted to show this empirically and visually, by comparing each map to the root map.

To the extent that the latter were true, it would formalize our intuition that the essence of redistricting can be thought of as the rubber band-like stretching of the boundaries of root districts to achieve a mix of policy goals, e.g., partisan fairness, competitiveness, etc. In other words, redistricting plans are fundamentally informed by the context of a state's population geography. Perhaps implicitly, one effectively has to start with the root districts and modify their boundaries.

Concept

We define the root map for a state that characterizes the population geography of a state as the districts of a valid map. Since it only depends on total population by precinct, it is the least information map — all other maps incorporate more information into their district boundaries. We generate an approximate root map for a state, using Balzer's Capacity-Constrained Voronoi Tessellations: Computation and Applications.3 In physics terms, these approximate root districts can be thought of as minimizing the moment of inertia or energy, or maximizing population compactness. The resulting districts are convex and not oddly shaped like other simple geometric approaches. These root districts characterize the population geography of a state, i.e., how many people live where.

Map drawers use lots of additional information — demographic data, election results, municipal boundaries, etc. — to, in effect, stretch these root district boundaries to achieve their desired mix of policy goals, e.g., more proportional, less county splitting, etc. Consequently, root districts are not only the implicit starting point for redistricting a state — redistricting does not start with a blank canvas! — but they can also be used to illustrate the tradeoffs inherent in redistricting a state.

Plan

Our plan mirrored our hypotheses:

  1. First, develop an automated method for generating approximate root districts — Justin Levitt had keyed Alec into the idea that root districts are maximally population compact (vs. geometrically compact), based on the physics concept of moment of inertia. Some searching led Alec to Andrew Spann, Dan Gulotta, Daniel Kane's work on the latter. Daniel Gulotta wrote a C++ implementation of their heuristic approach to support their paper "Electoral Redistricting with Moment of Inertia and Diminishing Halves Models" at MCM 07. Alec's plan was to simply reimplement it in Python.

  2. Then compare each notable map & official map to the root map for the state — Given the number of maps involved (252 = 42 x 6), Alec planned to develop a pipeline of tools to automate as much of the workflow as possible to produce the artifacts for this web site.

Of course, the latter depended on the former: without a well-defined, defensible root map, there would be no easy way to compare the notable maps for a state.

Scope

We chose to study the states apportioned two or more congressional districts in the 2020 census. Hawaii and Maine had to be skipped due to difficult data issues, leaving 42 states.

This analysis uses maps drawn in Dave's Redistricting. Besides the official maps used for the 2022 congressional elections, it uses the five notable maps for each state that have the highest ratings for proportionality, competitiveness, minority representation, compactness,

and county-district splitting. While these are not definitively the best on their respective dimensions (i.e., globally optimal), DRA users work hard to find maps that optimize these dimensions and have their map be selected as the notable map, so they are good proxies for maps that maximize these dimensions. As such, they serve to illustrate the tradeoffs between these quantifiable policy dimensions in a state.

For each state, we compare these six maps to the root districts we generated.

Method

At first Alec tried to reimplement Gulotta's C++ moment of inertia code in Python but met with only partial success. Fortunately, he shared what he was working on with his friend, Todd Proebsting, he got intrigued, and then Todd developed a solution based on Balzer's algorithm. The evolution of our heuristic approach for finding the lowest energy assignment of precincts to districts is described here.

To generate the root maps presented here, we ran this process 100 times for each state using random starting points and the 2020 Census VTD shapes and population data.4 Then we selected the lowest energy map that met three constraints:

  1. Contiguous
  2. Didn't split any precincts, and
  3. Had a population deviation of 2% or less

The specifics of our heuristic approach are not the main contribution of this study. Nor are the specific root maps we generated, though we think they are strong contenders for the lowest energy maps and interesting in their own right. The important contribution here is the idea of root districts that characterize population geography and what they reveal about other maps, the tradeoffs inherent in a state's political geography.

Data

The data used came from two sources.

DRA data:

Census data:

Due to the size of these files, none are stored in a GitHub repository, except the block-assignment files.

Workflow

Our overall workflow is described here.

Code

This site was developed using the code in three GitHub repositories:

The site is homed in the first. The code in that repository uses the code in the other two to generate root maps and analyze the official and notable maps relative to them.

Footnotes

  1. Compact Districts Aren’tFair. ↩

  2. See Baseline Congressional Districts: A Benchmark for Comparison. ↩

  3. It turns out, one cannot simply run a Voronoi algorithm over the precincts. There are lots of practical issues and real-world complications to deal with. ↩

  4. CA, OR, and WV don't have precincts (VTDs), so we used blockgroups instead like DRA. Also, the official Florida data is pretty messed up, so we used DRA's GeoJSON file of corrected Florida VTDs. ↩