GerryMath
gerrymath.org

Politicians are choosing their voters.

In a representative democracy, voters choose politicians — never the other way around. The inversion has a name, and it is now precisely measurable: a party-blind statistical test exists, courts have run it, and Congress has the power to require it. Run it yourself, on all fifty states, below.

"A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions." James Madison · Federalist No. 51 · 1788
Test Console — U.S. House Maps
INSTRUMENT 01 · EQUAL TILE PER STATE · OKABE-ITO SAFE PALETTE
READOUT → ✓ PASS 0 ! CAUTION 0 ✗ FAIL 0 – N/A 0
✓ PASS — inside the neutral range ! CAUTION — tilted, one-party pen, or untested new map ✗ FAIL — statistical outlier or abusive redraw – N/A — at-large single district Colors are Okabe-Ito colorblind-safe; every rating also carries a ✓ ! ✗ – symbol. Tap any state for its file.

Same ruler for both parties: FAIL currently includes Texas, Florida, Ohio and North Carolina and Illinois, Maryland, Oregon and post-Prop-50 California. First-pass ratings — methodology & caveats in the footer.

Exhibit A — How the trick works

Same voters. Three governments.

Twenty-five voters: 15 teal (60%), 10 magenta (40%). Every map below is legal — equal population, contiguous districts. Only the lines move.

Party Teal (15)   Party Magenta (10) — deliberately not red or blue.

“Cracking” shreds the minority party across every district; “packing” buries the majority in a few landslide seats. With the right lines, 40% of the voters govern 60% — no fraud, no stuffed ballots, just geometry. That is the entire scandal, and it is why the fix must be mathematical.

Exhibit B — the shapes

A field guide to the monsters

In 1812 a Boston engraver drew wings on a district map and named the beast for Governor Elbridge Gerry. The species never went extinct. The silhouettes below are not caricatures — they are the actual enacted boundaries, straight from U.S. Census geometry.

The Gerry-Mander: 1812 cartoon of a winged, clawed salamander drawn over the Essex South senate district of Massachusetts
The original, 1812. Elkanah Tisdale's "Gerry-Mander," Boston Gazette, March 26, 1812 — the Essex South district of Massachusetts, plus wings and claws. The joke that named the crime. (Public domain, via Wikimedia Commons.)

Every one of these was legal the day it was enacted; the ones that fell, fell on racial grounds — never partisan ones. And here is the caveat that cuts both ways: shape is neither necessary nor sufficient. The 1812 Essex district was built of whole towns, and Tennessee just dismantled Memphis with perfectly tidy lines. Ugly maps can be innocent and clean maps can be crimes — which is exactly why the verdict belongs to the ensemble statistics, not the eyeball. The monsters are the marketing. The math is the test.

The standard

The Outlier Test, in one sentence

Definition · v0.1

A congressional map is a gerrymander if its expected partisan outcome falls outside the middle 95% of thousands of computer-drawn maps that follow the same state's own neutral rules — equal population, contiguity, compactness, and intact communities.

The genius of the ensemble baseline is what it doesn't assume. It never demands proportional representation — single-member districts don't produce it and the Constitution doesn't require it. It never punishes geography: if one party's voters cluster in cities, the thousands of neutral maps cluster them too, and that natural tilt is built into the baseline. The only thing left for the test to catch is the thing we actually want to catch — intent, expressed as an outcome no neutral process would produce.

And it is enforceable. The algorithms (ReCom Markov chains) are open source. The 50-state ensembles are already published by academic teams. A judge doesn't have to weigh testimony about motive; she reads a percentile. In 2019 the Supreme Court said no "judicially manageable standard" existed. It exists. It ran in Pennsylvania's and North Carolina's courtrooms. It just needs to be written into law.

The instrument panel

Three levels of math, one verdict

Simple metrics sound the alarm. The ensemble delivers the verdict. No single napkin formula should ever decide a case alone — each one has known failure modes — which is exactly why the architecture is trigger → test.

Tier 1 · Napkin

Wasted votes

The efficiency gap: every losing vote, plus every winning vote past 50%+1, is "wasted." Net wasted votes ÷ total votes. Above ~7–8% (about two House seats), suspicion is warranted. Texas's 2025 map scores roughly R+17% — more skewed than 97% of maps in fifty years. Anyone with a spreadsheet can check it. Weakness: misfires in lopsided states.

Tier 2 · Symmetry

Mean–median & declination

Does the map treat 55% the same no matter who earns it? The mean–median gap and the declination angle read packing-and-cracking straight out of the sorted district results — no counterfactuals needed. Fast, party-blind screens; still gameable alone.

Tier 3 · The verdict

The ensemble outlier test

Generate thousands of maps under the state's own neutral rules; place the enacted map in that distribution. Inside the middle 95%: presumed fair. In the tail: convicted by its own geometry.

enacted map ▸
5,000+ neutral maps (blue) vs. the enacted map (vermillion). The tail tells the story.
Why now

The courts just left the field

Three rulings, one syllogism. As of spring 2026 there is effectively no federal judicial check on a congressional map.

Rucho v. Common Cause
2019 · 5–4

Partisan-gerrymandering claims are "political questions beyond the reach of the federal courts" — supposedly for want of a manageable standard. The Court pointed to one open avenue: Congress, under the Elections Clause.

Abbott v. LULAC
Apr 27, 2026 · summary reversal

Texas's mid-decade map stands. Its motive was partisan advantage "pure and simple" — and that, the Court confirmed, is permissible. Partisan intent is now an affirmative defense.

Louisiana v. Callais
Apr 29, 2026 · 6–3

The Voting Rights Act's Section 2 framework was rewritten; a state can now defeat a racial-gerrymandering claim largely by declaring its motive partisan. Justice Kagan, dissenting: Section 2 is "all but a dead letter."

Partisan claims: unreviewable. Racial claims: answerable with a partisan confession. Therefore the fix cannot come from a courtroom. It must be written into law — by Congress under Article I, §4, or into state constitutions. That is precisely what a bright-line statistical test makes possible.
TX +5RAug 2025 · upheld 4/27/26
MO +1RFall 2025 · referendum pending
NC +1ROct 2025
OH +2ROct 2025 · 12–3
CA +5DProp 50 · Nov 2025 · 64%
IN declinesSenate 31–19 · Dec 2025
KS declinesJan 2026
UT +1Dcourt-imposed fair map
CALLAIS · APR 29
FL +4Rsigned May 4
VA voidedstate SC · May 8
TN +1Rsigned May 7
SC declinesSenate · May 26
LA +1Rsigned May 29
AL +1R2023 map back · Jun 2
The 2025–26 arms race, net ≈ R+8 seats — roughly the entire margin of control of the U.S. House, decided by cartography rather than voters. Retaliation is the rational move in a rule-free game. Only a binding rule ends it.
Exhibit C — the price tag

Safe seats aren't free

Economics treats political competition the way it treats market competition: remove it, and quality falls, prices rise, and the customer absorbs the loss. The customer is you.

164 → 82 Swing seats, 1999 → 2023

Districts within ±5 points of the national vote have fallen by half (Cook PVI). For this November, analysts rate just 18 of 435 House races as toss-ups. In a safe seat the general election is decorative — the primary, a low-turnout contest of each party's most polarized sliver, is the whole ballgame.

Cook Political Report PVI archive; race ratings, June 2026
≈20% Income effect of political competition

Where one party can't lose, policy drifts anti-growth — higher taxes, lower capital spending. Besley, Persson & Sturm estimate the competition unleashed in Southern states raised long-run income per capita by about a fifth. Their natural experiment for competition's value? The Voting Rights Act — the statute Callais just hollowed out.

Besley, Persson & Sturm, Review of Economic Studies (2010)
$10M+ One state's map-defense bill

North Carolina taxpayers: roughly $7M in redistricting legal fees through 2018, ~$3M more for the 2021-cycle suits — about 40 lawsuits in 30 years. Alabama's post-Callais special primary alone costs $4.45M. Nationally, post-2020 maps have drawn 100 lawsuits across 30 states.

Winston-Salem Journal; NC Newsline; Alabama LFO; Brennan Center tracker

Full disclosure, because this site runs on it: Cook's own analysis attributes roughly four-fifths of the swing-seat collapse to voters sorting themselves, not to line-drawing. But the isolating comparison is damning — in states where independent commissions hold the pen, swing seats fell 39% since 1997; where one party's legislature holds it, 70%. Gerrymandering doesn't cause the sorting. It converts the sorting into a padlock — and the padlock, unlike the sorting, is something a law can remove.

The fix — graded for the real world

Four phases from disclosure to disarmament

Nobody passes utopia in one vote. Each phase is independently useful, independently passable, and already has a working precedent.

Disclosure

Every enacted congressional map must publish its efficiency gap, mean–median, declination, and ensemble percentile, computed by a public open-source tool. Costless, party-blind, and very hard to vote against.

Precedent: PlanScore and the Princeton report cards already do this voluntarily for every map.

Presumption

A map outside the middle 95% of its ensemble is presumed invalid; the burden shifts to the state to prove geography compelled it. Rebuttable, so honest outliers survive.

Precedent: the Freedom to Vote Act (2021–22) — a 1-seat / 7% trigger over four statewide elections. It passed the House and died to a filibuster.

Bright line + automatic remedy

Fail the test and a court or special master adopts the median ensemble map — no endless redraw ping-pong — plus a flat ban on mid-decade redistricting.

Precedent: Pennsylvania (2018) and Utah (2026) courts adopted remedial maps; Ohio shows what happens without an automatic remedy.

Structure

Independent commissions hardened against override — because California's Prop 50 proved even a model commission can be suspended by one ballot measure when the arms race demands it.

Precedent: AZ, CO, MI commissions rate PASS on this page every year they've existed. The hardening is the missing piece.
The stakes

A Madisonian nightmare, on schedule

Madison's machine has one load-bearing part: ambition counteracting ambition, with the general election as the counterweight. Gerrymandering removes the counterweight. When the district is drawn safe, the general election is theater and the primary is the only election that counts — decided by the most polarized sliver of one party. Representatives stop answering to constituents and start answering to mapmakers. Entrenchment compounds every cycle, and the parties come to serve their own preservation over the country. That is not a slippery-slope warning; it is the observed trajectory of the states marked ✗ above.

"Who are to be the electors of the federal representatives? Not the rich, more than the poor... The electors are to be the great body of the people of the United States." James Madison · Federalist No. 57 · 1788

Madison knew this fight personally. In 1788, Patrick Henry's Anti-Federalist legislature set Virginia's 5th District lines and recruited James Monroe to keep Madison out of the First Congress — the only House race ever between two future presidents. Modern scholarship shows the district itself was compact whole counties, so the popular "first gerrymander" label overreaches; the documented part is the intent. Madison won anyway, then spent Federalist 51 warning that dependence on the people needs "auxiliary precautions."

The Outlier Test is an auxiliary precaution — a parchment barrier upgraded to arithmetic. It doesn't trust mapmakers' motives, either party's, ever. It just measures.

What you can do

The math is done. The law isn't.

Three moves, in order of leverage: tell your representative and senators to revive the redistricting title of the Freedom to Vote Act with an ensemble standard; if your state is one of the ~26 with citizen initiatives, back a hardened-commission measure; and support the people who built the instruments.

Instruments · nonpartisanPlanScore
Scores any map on four fairness metrics, free.
Instruments · nonpartisanData & Democracy Lab (MGGG)
Built GerryChain, the open-source ensemble engine.
Instruments · nonpartisanALARM Project
5,000 simulated plans per state, published openly.
Instruments · nonpartisanDave's Redistricting
Draw and score your own state's map tonight.
ScorekeeperPrinceton Gerrymandering Project
A–F report cards; grades both parties' maps F when earned. Donate via the Electoral Innovation Lab.
Law & litigationCampaign Legal Center
Won the Utah fair-map fight; drafts model statutes.
Law & litigationBrennan Center
Tracks every map and wrote the book on the fix.
GrassrootsCommon Cause · RepresentUs · LWV
The initiative campaigns run through these three.
Find your representative Re-run the test ↑