Gerrymandering: The Math Behind the Maps

Gabrielle Birchak/ April 18, 2025/ Contemporary History, Future History, Modern History/ 0 comments

Wel­come to Math! Sci­ence! His­to­ry! I’m Gabrielle Bir­chak and today, we’re div­ing into a top­ic that is as math­e­mat­i­cal as it is polit­i­cal: ger­ry­man­der­ing. It’s a prac­tice that has shaped Amer­i­can democ­ra­cy for over 200 years, influ­enc­ing elec­tions, pow­er, and rep­re­sen­ta­tion. But did you know that math and sci­ence are key tools in both cre­at­ing and fight­ing ger­ry­man­der­ing? Today, we’ll explore the his­to­ry, the math­e­mat­i­cal con­structs behind it, and how peo­ple can take action to cre­ate fair­er elec­tions. Let’s get started.

What is Gerrymandering?

Before we break down the math and sci­ence behind it, let’s define ger­ry­man­der­ing. It’s the prac­tice of manip­u­lat­ing the bound­aries of elec­toral dis­tricts to favor one polit­i­cal par­ty over anoth­er. It gets its name from Elbridge Ger­ry, a gov­er­nor of Mass­a­chu­setts who, in 1812, approved a dis­trict shaped like a sala­man­der. A polit­i­cal car­toon­ist dubbed it a ‘Ger­ry-man­der,’ and the name stuck. Today, it remains a major tool for polit­i­cal par­ties to con­trol elections.

The His­to­ry of Gerrymandering

Ger­ry­man­der­ing is near­ly as old as Amer­i­can democ­ra­cy itself. In the 19th cen­tu­ry, politi­cians redrew maps to weak­en oppo­nents. How­ev­er, in the 20th cen­tu­ry, redis­trict­ing became more pre­cise, with politi­cians using cen­sus data to sup­press cer­tain vot­ing blocs. After the Vot­ing Rights Act of 1965, racial ger­ry­man­der­ing became more scru­ti­nized, but par­ti­san ger­ry­man­der­ing per­sist­ed. In 2019, the Supreme Court ruled in Rucho v. Com­mon Cause that fed­er­al courts can­not decide cas­es on par­ti­san ger­ry­man­der­ing, mak­ing state action more impor­tant than ever.

The Math of Gerrymandering

Now, let’s talk num­bers. Ger­ry­man­der­ing relies heav­i­ly on math­e­mat­i­cal prin­ci­ples. One of the sim­plest ways to mea­sure ger­ry­man­der­ing is by look­ing at com­pact­ness. A dis­trict should ide­al­ly be as com­pact as pos­si­ble, but ger­ry­man­dered dis­tricts are often odd­ly shaped. Sci­en­tists use dif­fer­ent math­e­mat­i­cal tests to mea­sure this, such as:

• Pols­by-Pop­per Score: A ratio com­par­ing a district’s area to the area of a per­fect cir­cle. The clos­er to 1, the more com­pact; the clos­er to 0, the more suspicious.
• Schwartzberg Ratio: Com­pares the perime­ter of a dis­trict to a circle’s perime­ter of the same area.
• Reock Score: Mea­sures how much of a district’s area fits with­in the small­est pos­si­ble cir­cle around it.

Let’s take an exam­ple: North Carolina’s old 12th Con­gres­sion­al Dis­trict once had a Pols­by-Pop­per Score of just 0.017—a clear indi­ca­tion that it was manipulated.

How Ger­ry­man­der­ing Works: Pack­ing & Cracking

There are two main strate­gies used in gerrymandering:

• Pack­ing: This con­cen­trates oppo­si­tion vot­ers into one or a few dis­tricts, wast­ing their votes.
• Crack­ing: This spreads oppo­si­tion vot­ers across mul­ti­ple dis­tricts, dilut­ing their vot­ing power.

For exam­ple, imag­ine a state with 60% Democ­rats and 40% Repub­li­cans. In a fair map, dis­tricts would reflect that ratio. But with ger­ry­man­der­ing, dis­tricts could be drawn so that Repub­li­cans con­trol most of the seats despite being the minor­i­ty! That’s the pow­er of math­e­mat­i­cal manip­u­la­tion in politics.

The Sci­ence Behind Gerrymandering

Beyond math, com­put­er sci­ence has rev­o­lu­tion­ized ger­ry­man­der­ing. Polit­i­cal map­mak­ers use machine learn­ing and data mod­el­ing to draw maps that favor their par­ty. These algo­rithms use demo­graph­ic data, vot­er his­to­ry, and even social media trends to pre­dict how peo­ple will vote.

But the same tech­nol­o­gy is being used to fight ger­ry­man­der­ing. Researchers at Prince­ton and Har­vard have devel­oped auto­mat­ed redis­trict­ing algo­rithms to cre­ate fair maps. These com­put­er-gen­er­at­ed maps serve as a bench­mark to deter­mine whether offi­cial maps are extreme outliers.

Real-World Cas­es of Gerrymandering

Let’s look at some of the most noto­ri­ous ger­ry­man­der­ing cas­es in South­ern states:

1. Gomil­lion v. Light­foot (1960, Alaba­ma) – Alaba­ma redrew the city of Tuskegee’s map to exclude near­ly all Black vot­ers. The Supreme Court ruled this was uncon­sti­tu­tion­al racial gerrymandering.
2. Shaw v. Reno (1993, North Car­oli­na) – The Court ruled that race-based dis­trict­ing is uncon­sti­tu­tion­al unless there is a com­pelling reason.
3. Abbott v. Perez (2018, Texas) – Texas was found to have drawn maps that dis­crim­i­nat­ed against Lati­no voters.
4. Allen v. Mil­li­gan (2023, Alaba­ma) – The Supreme Court ruled that Alabama’s con­gres­sion­al map vio­lat­ed the Vot­ing Rights Act by dilut­ing Black vot­ers’ influence.

Each of these cas­es high­lights how ger­ry­man­der­ing affects real communities.

Ger­ry­man­der­ing Around the World

Ger­ry­man­der­ing isn’t just a prob­lem in the U.S. Let’s take a look at how oth­er coun­tries han­dle it:

• Unit­ed King­dom – The UK has an inde­pen­dent Bound­ary Com­mis­sion that redraws dis­trict lines every 8–12 years, reduc­ing polit­i­cal interference.
• Cana­da – Cana­da also uses inde­pen­dent com­mis­sions, a reform that end­ed past ger­ry­man­der­ing practices.
• Aus­tralia – Australia’s inde­pen­dent elec­toral com­mis­sions pre­vent ger­ry­man­der­ing, though malap­por­tion­ment used to favor rur­al areas.
• India – India’s Delim­i­ta­tion Com­mis­sion is meant to be inde­pen­dent, but polit­i­cal influ­ence still plays a role.
• Rus­sia – While Rus­sia doesn’t rely on ger­ry­man­der­ing in the same way, oth­er forms of elec­toral manip­u­la­tion, like vot­er sup­pres­sion, take place.

Many democ­ra­cies have inde­pen­dent com­mis­sions to ensure fair redistricting—something that some U.S. states are begin­ning to adopt.

How Can We Fight Gerrymandering?

Ger­ry­man­der­ing may seem over­whelm­ing, but there are ways to fight back. Here’s how:

1. Sup­port Inde­pen­dent Redis­trict­ing Com­mis­sions – States like Michi­gan and Cal­i­for­nia have suc­cess­ful­ly removed politi­cians from the map-draw­ing process.
2. Push for State-Lev­el Legal Chal­lenges – Some state supreme courts, like Pennsylvania’s, have struck down unfair maps.
3. Sup­port Fed­er­al Leg­is­la­tion – Bills like the For the Peo­ple Act (H.R.1) and the John Lewis Vot­ing Rights Act could estab­lish nation­al protections.
4. Use Data & Tech­nol­o­gy – Tools like Dave’s Redis­trict­ing App and PlanScore allow vot­ers to ana­lyze dis­trict maps.
5. Vote in State Elec­tions – Since state leg­is­la­tors con­trol redis­trict­ing, vot­ing in these elec­tions is crucial.
6. Advo­cate for Bal­lot Ini­tia­tives – In states that allow it, push­ing for redis­trict­ing reform via bal­lot mea­sures can be an effec­tive strategy.

Orga­ni­za­tions like Com­mon Cause and the Bren­nan Cen­ter for Jus­tice are work­ing to fight gerrymandering—getting involved or donat­ing can make a real difference.

Con­clu­sion: The Pow­er of the People

Ger­ry­man­der­ing is a polit­i­cal prob­lem, but math and sci­ence pro­vide the tools to expose and fix it. While politi­cians may try to manip­u­late dis­trict lines, vot­ers, activists, and researchers have the pow­er to fight back. It takes aware­ness, advo­ca­cy, and par­tic­i­pa­tion at all lev­els of government.

PODCAST SHOW NOTES: 

🔎 Episode Overview
In this episode of Math, Sci­ence, His­to­ry, we explore one of the most qui­et­ly pow­er­ful forces in Amer­i­can democ­ra­cy: ger­ry­man­der­ing. From its ori­gin over 200 years ago to its impact on today’s elec­tions, ger­ry­man­der­ing is both a polit­i­cal weapon and a math­e­mat­i­cal puzzle.

We break down the math­e­mat­i­cal­prin­ci­ples used to detect ger­ry­man­der­ing, explore real court cas­es in South­ern states, and exam­ine how com­put­er sci­ence and vot­er data are used to both draw and fight unfair dis­tricts. You’ll also learn how oth­er coun­tries han­dle redistricting—and what the U.S. can learn from them.

Whether you’re a math geek, a sci­ence lover, or just a con­cerned cit­i­zen, this episode gives you prac­ti­cal tools and knowl­edge to take action against one of the most manip­u­la­tive prac­tices in mod­ern politics.

✅ 3 Things You Can Do to Stop Gerrymandering

Sup­port Inde­pen­dent Redis­trict­ing Com­mis­sions
Advo­cate for fair dis­trict­ing in your state by sup­port­ing or start­ing ini­tia­tives to cre­ate non­par­ti­san redis­trict­ing commissions.

Use Data Tools to Ana­lyze Your Dis­trict
Explore your vot­ing maps using free tools like Dave’s Redis­trict­ing App or PlanScore to see if your dis­trict is gerrymandered—and share your find­ings with your community.

Vote in State and Local Elec­tions
Remem­ber, state leg­is­la­tors often con­trol the redis­trict­ing process. Vot­ing in state and judi­cial elec­tions is one of the most pow­er­ful ways to influ­ence how future maps are drawn.

📚 Resources to Learn More About Gerrymandering

Bren­nan Cen­ter for Jus­tice – Redis­trict­ing & Ger­ry­man­der­ing
In-depth arti­cles, research, and legal updates on redis­trict­ing and vot­ing rights.

Prince­ton Ger­ry­man­der­ing Project
Offers tools, research, and non­par­ti­san analy­sis for cre­at­ing and eval­u­at­ing fair dis­trict maps.

FiveThirtyEight’s Ger­ry­man­der­ing Explain­ers
Data jour­nal­ism and inter­ac­tive pieces explor­ing how ger­ry­man­der­ing affects elections.

📖 Books

Ratf**ked: The True Sto­ry Behind the Secret Plan to Steal Amer­i­ca’s Democ­ra­cy by David Daley
An inves­tiga­tive look into how ger­ry­man­der­ing has shaped U.S. pol­i­tics post-2010.

Draw­ing the Lines: Con­straints on Par­ti­san Ger­ry­man­der­ing in U.S. Pol­i­tics by Nicholas R. Seabrook
A deep­er aca­d­e­m­ic and legal dive into how redis­trict­ing works and how it’s abused.

🔗 Explore more on our web­site: mathsciencehistory.com

📚 To buy my book Hypa­tia: The Sum of Her Life on Ama­zon, vis­it https://a.co/d/g3OuP9h

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