Black representation and district compactness in Southern congressional districts

ABSTRACT

This paper explores the assumed trade-off between district compactness and Black representation in legislative districts in the American South. We analyze heuristically generated districts using current US demographics and historical congressional maps since the 1970s. Computations are performed using an iterative heuristic to find feasible solutions guided by multiple objectives. We find that while the trade-off has been strongly observed historically, it is possible to effectively address both goals simultaneously in most cases. We can demonstrate maps substantially superior to the present enacted maps on both dimensions in at least seven of the nine states analyzed. Nevertheless, the trade-off appears more necessary in states with larger and/or more heavily rural Black populations than in more urbanized states, where the drawing of compact Black-influence districts is easier.

KEYWORDS:

• Legislative; racial politics; American politics; elections; minority representation; political representation; redistricting

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Note that the map in the bottom-right corner of Figure 1 was overturned in Cooper v. Harris. While this map contains many extremely noncompact districts, it was replaced by a much more esthetically pleasing map in the bottom middle of the figure, which nevertheless resulted in a delegation with identical racial and partisan composition during its two cycles in effect.

2 While our approach is similar to simulated annealing, it relies on a more extensive use of large steps to avoid local optima. These large steps give wide variation in the maps produced, rendering the more computationally-intensive approaches of tabu search and genetic algorithms unnecessary.

3 Census block groups are geographical units used by the US Census containing an average of 39 census blocks, with populations between 600 and 3,000 people. Block groups are the smallest unit for which we have found it possible to effectively and feasibly generate maps. Other works generating maps by algorithm generally either use block groups (e.g., Cirincione, Darling, and O'Rourke 2000), or somewhat larger precincts (E.g., Chen 2017; Duchin 2018; Becker et al. 2021; Borodin 2022) or census tracts (Saxon 2020).

4 A detailed description of this can be found in Duchin (2018), and open-source implementation of the code is available in GerryChain (github.com/mggg/GerryChain).

5 Although not yet prominent in political science scholarship or jurisprudence, the graph-theory based “cut edges” measure of compactness has also become increasingly common in the computational literature. Although we do not directly optimize on this measure, the within-state correlation between cut edges and Polsby-Popper compactness in our simulation dataset is .96, and thus maps that perform well on one measure almost universally also perform well on the other. While Reock compactness and other more recently proposals, such as population-weighted measures, cannot be as efficiently evaluated computationally by our algorithm, and thus are not feasible objectives at our scale, we also believe our compactness objective has face validity in generating consistently compact districts even when judged subjectively, as shown in the Objective 1 and 2 maps for all states in Figure 8.

6 These models also idiosyncratically incorporate other demographic variables (e.g., % of government workers in Lublin et al.), but none are found to have consistently significant effects on Black representation. Some models also incorporate campaign-specific variables (e.g., open seats in Hicks et al.) that would be inappropriate or impractical to include in the context of generalizing about hypothetical future elections. Also, Becker et al. (2021) take issue with this canonical method, instead using ecological inference and precinct-level election data to estimate which candidates in statewide elections in Texas were the preferred choice of Black and Latino voters. While this method more directly measures minority voter preferences among the existing candidate field, it is not itself a measure of Black descriptive representation and does not address supply-side conditions of when Black candidates choose to run.

7 To account for potential serial correlation over time in a given district, House races are clustered by district crossed with decade, though this affects only standard errors of the estimates and not the coefficients.

8 Throughout this paper, we refer to districts with at least 50% BVAP as “Black-majority” and districts with at least a 50% probability of electing a Black representative (often in the 40–50% BVAP range) as “Black opportunity”. These definitions are not intended to reference or suggest a legal standard for application to the Gingles test or other related litigation, and are not explicitly maximized by our objective functions. Estimating Black representation probabilistically, rather than assessing districts in a binary or categorical way as Black-majority or Black-opportunity districts, allows the algorithm to account for unusual events such as the election of a Black Republican in FL-19 (7% Black) or a White Democrat in TN-09 (66% Black).

9 Thus, in Maryland, for example, it would favor two 45% Black districts (each with a 70% chance of Black representation) over one 65% Black and one 25% Black district (with 99% and 8% chances of Black representation, respectively).

10 Both compactness and proportionality measures for congressional maps in all fourteen Southern states since the 1970s are shown in Appendix A. Compactness data are drawn from the map used in the first election of the decade; measures for mid-decade map changes are not shown.

11 Compactness also falls in the 2010s. Anecdotally, this is likely the result of increasingly extreme partisan gerrymanders during this decade, a factor not explored in this article.

12 For example, Mississippi was 36.8% Black in the 1980 census. For six years during the 1980s, one of the state's representatives was Black, with no Black representatives the other four years. Thus, the delegation averaged 12% Black, and the racial proportionality of the Mississippi delegation in the 1980s is -24.8%. Among all Southern states’ congressional maps from the 1970s through 2010s, the overall correlation between racial proportionality and Polsby-Popper compactness is -.28.

13 Through a series of benchmarking trials, we determined a run length of 25,000 steps provided the optimal balance for the efficient generation of maps; see Appendix B for discussion.

14 Formally, a Pareto frontier is the subset of all solutions (measured on two or more measurements) in which it is not possible to find an alternate solution which improves on one measurement without simultaneously decreasing another measurement. A Pareto curve is a visual depiction of the Pareto frontier set along two or more dimensions. However, we use the term more casually to describe the curves showing the approximate 50th and 90th percentile results of each objective function in Figure 5 and 7, respectively. As described in Section VI, the shape of these curves can be used to evaluate the extent to which compactness and Black representation are mutually exclusive in a given state. See Altman and McDonald (2018) for another use of Pareto curves to evaluate trade-offs in redistricting norms.

15 “Best” and “median” are defined by ranking the 100 maps generated for each objective function by their objective function value.

16 The “Non-Spatial Optimum” is meant to provide a theoretically (but usually wildly unrealistic) absolute ceiling on Black representation in the state. Its bounds were computed using the following optimization model: where $V,B$, and $N$ are the total number of voters, Black-voters, and non-voters in the region, respectively and $\stackrel{\stackrel{~}{}}{P}={\displaystyle \frac{V+N}{\left|J\right|}}$ is the number of people that each district is meant to contain. Then $y_j$ and $z_j$

are the number of black voters and total voters in district j, respectively. ${\zeta }_j$ is the number of non-voters in district j. These solutions were obtained by employing an optimization model that was implemented in the integer programming solver GUROBI.

17 Across all nine states, 20.45 Black members would be elected out of 80 total seats if Black voters were represented proportionally. Our formula estimates than an average of 14.37 Black members would be elected under the maps enacted following the 2020 census; this compares closely to the 14.2 Black members actually elected on average during the 2010s (across 79 districts).

18 The curve can also be defined using the means of the top quintile of runs, or some other subset, with substantively very similar results.

19 We explore trade-offs in partisan gerrymandering using this method in Goedert et al. (2024).