Compact Districts Aren’t Fair

More precisely, compact districts aren’t always fair. In fact, increasingly they are not. Similarly, gerrymandered districts don’t always have unusual animal-like shapes, and increasingly they don’t.

This post introduces the concept of political geography and explains how it interacts with measures of compactness & fairness. There are two key takeaways:

• Compactness is frequently not a politically neutral criterion, and
• Gerrymandering is not always about district shapes—The essence of gerrymandering is packing & cracking the likely voters for one party to gain political advantage for the other party.

Gerrymander porn gets all the attention, with cute shapes, alphabet glyphs, and crafty names. To make sure that you’re not distracted by it, use analytics that measure partisan bias (see Evaluating Partisan Performance).

As you’ll see, mapmakers can make what would be fair compact districts unfair with contorted shapes (“gerrymandering”), and they can make what would be unfair compact districts fair more fair with less compact shapes (“remediation”).

Political Geography

The key concept to understand is political geography, by which I mean the distribution of different kinds of voters throughout a state.

• At one extreme, likely Republican & Democratic voters might be uniformly distributed across a state. In this case, each area within the state would be a microcosm of the statewide political proportions. You can think of states like this as having a relatively homogenous political geography.
• At the other extreme, likely Democratic & Republican voters might distributed very unevenly throughout a state. The various areas within a state would have quite different makeups from the statewide proportions. You can think of states like this as having a relatively heterogenous political geography.

For quite some time people in many states of been self-sorting into urban centers (mostly Democratic-leaning voters) and rural areas (mostly Republican-leaning voters).¹ As you’ll see, this typically makes compact districts in those states unfair. Political scientist Jonathan Rodden has written an entire, easy-to-read book that explores how & why this clustering confers political advantage to one party.²

Compactness vs. Fairness

To show that compact districts are not always fair & vice versa, I’ll use a pair of congressional maps from two states: North Carolina (NC) and Pennsylvania (PA).³ They illustrate these four possibilities.

I’ll start with the easy case where compact districts happen to be fair due to political geography and walk you through the other three cases.

NC Fair & Square

This congressional map for NC is both very compact and very fair (upper right quadrant in the figure above).⁴

Relatively compact districts are relatively fair in NC

Average compactness of this map is rated 77 of 100 using the common mathematical metrics of Reock (0.4874) and Polsby–Popper (0.3214), and people naturally just the compactness of these districts to be 68 of 100. We call this “know it when you see it” compactness (KIWYSI).⁵ Note: All ratings below are [0–100] where bigger is better.

Given the typical statewide vote shares in NC, a 7–6 Republican–Democratic split would be closest to proportional. In this map, the likely number of Democratic seats is 5.81, making disproportionality just 1.49%. Proportionality rates 98 of 100.⁶

NC has a fairly homogenous political geography where these relatively compact districts yield a relatively fair map.

NC 116th Official

The official NC map for the 116th Congress drawn by the state legislature was quite a bit different though, reflecting a classic explicit gerrymander (lower left quadrant) where the district shapes have been intentionally contorted for political advantage.

Relatively non-compact districts are very unfair in NC

Here, the average compactness is rated just 36 mathematically (Reock: 0.3373, Polsby–Popper: 0.2462) and judged just 42 by people. As a result of these contortions, the likely number of Democratic seats is just 3.55. Disproportionality is 18.87%, and proportionality rates just 11.

The same political geography has been carved up into non-compact districts so that the map is very unfair.

PA Compact

The political geography of PA is much more heterogenous. The cities of Philadelphia and Pittsburgh have distinctly different political profiles from the rest of the state (and vice versa).⁷

This map for PA⁸ is very compact, rated 86 mathematically (Reock: 0.4443, Polsby–Popper: 0.4734) and judged 83 by people.

Very compact districts are very unfair in PA

While the typical statewide Democratic vote share of 52.80% in PA means that a 10–8 Democratic–Republican split would be closest to proportional, the likely number of Democratic seats in this map is just 8.43. The disproportionality is only 8.73%, but the map is so unfair as to be antimajoritarian, giving more seats to Republicans than Democrats. Hence, the proportionality rating is zero.

This map would be what I call an implicit gerrymander involving acts of omission: intentionally not distorting district shapes to mitigate a state’s naturally skewed political geography (upper left quadrant).⁹

Compacts maps are not always fair. Sometimes they are very unfair!

PA 116th Official

Finally, the official map for the 116th Congress in PA illustrates that mapmakers — in this case, the Pennsylvania Supreme Court — can explicitly remediate (i.e., reduce) the discriminatory harm resulting from the state’s political geography (lower right quadrant).

Relatively fair districts in PA are not very compact

In this map, average compactness is rated 64 mathematically (Reock: 0.4279, Polsby–Popper: 0.3271) and is judged 59 by people. This map is not as compact as the previous one.

However, the likely number of Democratic seats is 9.20. Disproportionality is just 4.46%, so proportionality rates 78. In other words, some compactness has been traded off for more fairness.

Conclusion

I’ll leave you with two thoughts:

• Compactness is frequently not a politically neutral criterion — Depending on the political geography of a state, compact districts can actually be quite unfair politically, as you saw in the case of PA above. This is increasingly so in states, due to the urban/rural sort of Democratic/Republican-leaning voters.
• Gerrymandering is not always about district shapes — Classically gerrymandering was synonymous with crazy district shapes, because mapmakers had to pack & crack partisans from relatively homogenous political geographies into complex district shapes to achieve political advantage. As you saw above though, compact districts tend to do the same thing when a state’s political geography is distinctly sorted along urban/rural lines. Compact districts can pack & crack partisans just as effectively as wild shapes in previous times. The essence of partisan gerrymandering has always been about engineering the composition of districts for political advantage (i.e., to make them unfair).

Don’t get distracted by district shapes; focus on how fair they are (see Evaluating Partisan Performance).

Caveats

I need to acknowledge a few things:

1. There are many mathematical measures of the degree to which district shapes are compact — I used two of the most common ones, Reock and Polsby–Popper. I also showed scores that reflect how people naturally judge the compactness of district shapes.⁵
2. Similarly, there are many possible ways to measure the degree to which a redistricting plan is fair — I used the simple intuitive notion of proportional representation: If a party gets 50% of the statewide votes in an election, they should win 50% of the seats, and, more generally, the seat share should track the vote share. There are many more sophisticated (and complex) ways to measure bias.¹⁰
3. There are also other important factors to consider when drawing districts — These include competitiveness, the opportunity for minority representation, and how much communities of interest (COI) and political subdivisions (like counties, cities, etc.) are split. I ignored these, so I could make my point.

None of these caveats contradict (or even diminish) the main thrust of this post, but it’s important to be clear about the complexity of redistricting. Here I focused in on the interplay between compactness & fairness, because many people erroneously conflate the two.

A final wrinkle: At the same time that compactness & fairness are being traded off in the examples above, keep in mind that the metrics for the other criteria are also changing. For example, making a set of districts more compact might require you to split more counties. Redistricting is a complex, multidimensional problem!

Footnotes

1. See The Big Sort (Bishop 2011).
2. See Why Cities Lose (Rodden 2019).
3. All four maps use the official 2010 census population and the our election composite for that state.
4. Map by DRA user ‘coachjimfox’. See Fox, James. 2021. Fair and Square Redistricting. APSA Preprints. doi: 10.33774/apsa-2020–5vg8w-v2.
5. See How to Measure Legislative District Compactness If You Only Know it When You See It for details.
6. See Proportionality.
7. See Pennsyktucky.
8. Map by DRA user ‘theodoriC’.
9. See The Lesser-Known Way to Gerrymander.
10. See Two Definitions of “Fair”.