Simulated Redistricting Maps as a
Baseline
Five Thousand Maps Nobody Drew
Democracy’s Data
Last updated September 15, 2026 at 4:42p EDT
A gerrymandered congressional district can look perfectly tidy, and
an innocent one can look like a spilled drink. Rivers wander, county
lines wander, and some of the strangest districts in America were drawn
strangely in order to keep one community inside one seat. The eye is a
poor instrument here. So how do you tell a gerrymander from a map that
merely looks odd?
You need something to hold the map against. Not an ideal map, which
nobody can define, but the ordinary range: the maps a process with no
interest in the outcome would have produced. Nobody drew those maps,
because nobody had any reason to. This brief uses five thousand of them
per state, drawn by a computer, and asks where each state’s real map
falls among them. That position is the evidence. A map inside the range
is unremarkable however it looks, and a map far outside it has something
to explain.
The test
Using the ALARM Project’s 50-State Redistricting
Simulations, a collection built by a research group at Harvard
led by Kosuke Imai, described at https://alarm-redist.org/fifty-states/ and published on
the Harvard Dataverse at https://doi.org/10.7910/DVN/SLCD3E. For every state with
more than one congressional district it supplies two things side by
side. One is the enacted plan, the map the state
actually put in force after the 2020 census. The other is 5,000
alternatives drawn by a program that never saw a voter’s party or a
resident’s race. That program had three rules: equal
population between districts, districts in one connected piece, and
districts that are not needlessly sprawling. Call the second set the
neutral maps, and the 5,000 of them taken together the
ensemble.
That pairing is why this source rather than another. Being unusual is
a statement about a distribution, not about a map, and no single plan
carries a distribution. This is the collection that ships one beside the
enacted plan for every state at once.
Two files meet here, and each count below is a join.
The enacted plan and the ensemble are separate objects that agree on
nothing but the state’s postal code and the district numbers inside it.
Match them on that, and you can subtract. Join Keys and
Crosswalks works the mechanics of exactly that kind of match, and
the repair for a key that misbehaves: a crosswalk, a table that
translates one set of areas into another. The assumption this join
quietly adds is that the two files describe the same electorate under
the same rules, differing only in where the lines went.
The data
Almost nothing you will read below arrives in the download. Every
count is computed from it, and the definitions are where the argument
lives.
A district counts as competitive if its two-party
vote share lands within some number of points of an even split. The
two-party share is the Democratic votes divided by the Democratic and
Republican votes together, third parties set aside.
competitive_national.csv carries one row per
threshold, at 2.5, 5, 10 and 15 points, with
enacted and neutral_mean beside it.
competitive_by_state.csv repeats all of that per
state, with n_districts.
A district counts as Black-plurality if Black
voting-age population is the largest of every racial and ethnic group
reported for it. That is stricter than “more Black residents than
white,” which can be true in a district where Hispanic residents
outnumber both. An earlier version of this brief used the looser test
and misclassified several genuinely Hispanic-plurality districts. The
error was caught by comparing the national count against an independent
tally, which is worth doing to any number of this kind.
black_by_state.csv gives each state
actual_black, neutral_black_mean and
gerry_black, plus n_plans_tied_at_max. That
last column matters. Thousands of the 5,000 plans are usually tied for a
state’s highest possible Republican seat count, and
gerry_black takes whichever of those tied plans holds the
fewest Black-plurality districts. Read Texas’s row to see the three
numbers made. Its enacted map holds 2 Black-plurality districts. Count
the same way in each of the 5,000 neutral maps and the average is 0.21,
which means most of them hold none. 8 of the 5,000 tie for the highest
Republican seat count any of them reaches, and gerry_black
is whichever of those 8 holds the fewest Black-plurality districts: 0.
It is not a real gerrymander anybody drew. It is the most adversarial
map available inside an ensemble that was never told to be adversarial
about race.
Two cleaning decisions travel with the numbers. Six states have one
House seat and so nothing to simulate, leaving 44 states and 429
districts everywhere below. And Alabama’s and Louisiana’s enacted counts
carry a hand correction, because courts ordered new maps after the
dataset’s own snapshot.
Before you scroll, make two predictions. If district
lines were drawn by a process blind to party, would there be more
competitive seats than there are today, or about the same? And would
that hold in every state, or only in most of them?
What it says about democracy
Figure 1. Neutral maps produce more competitive districts, at
every threshold checked. A dumbbell, because the question is a
distance: two counts of the same thing, and the gap between them is the
whole finding. Across 44 states and 429 districts, the enacted maps hold
79 districts within five points of even against a neutral average of
108.8, about 1.38 times as many.
That consistency is the point. One threshold could be an accident of
where the line falls. Four thresholds moving the same direction by
comparable margins is a fact about the country’s districts, not a choice
about a cutoff.
Figure 2. Texas carries the largest gap of any
state. Its enacted map holds 2 districts within five points of
even out of 38, where the neutral maps average 8.7 — more than four
times as many. No other state comes close.
The exceptions are the interesting part. Illinois and California sit
next on that list, so the pattern is not one-sided, though states with
Republican-controlled legislatures dominate the largest gaps. Illinois
was drawn by its legislature. California was drawn by an independent
commission, and its map is third in the country for distance from its
own neutral ensemble. In 9 states a commission’s map becomes law without
a legislative vote, and most of those states sit close to their
ensembles. California says a commission is not a machine for producing
the neutral map.
The lines decide something besides competition. Section 2 of the
Voting Rights Act forbids lines that dilute a racial minority’s ability
to elect the candidates it prefers. The neutral maps allow a sharper question
than whether a given state diluted anyone. They allow you to ask what
happens to Black representation when a legislature stops trying to
preserve it and tries instead to win every seat the lines can yield.
The next figure is restricted to the 20 states Republicans controlled
after the 2020 census. A Republican gerrymander is only a live
possibility where Republicans hold the pen, and running the same test on
a Democratic-controlled state would ask about a map nobody there has a
reason to draw.
Figure 3. Georgia is the only state that keeps a
Black-plurality seat under a maximized gerrymander. Across
those states the enacted maps hold 14 Black-plurality districts and the
neutral maps average 5.3. The most adversarial map inside the
simulations holds 2, a cut of about 86%. Every state with exactly one
such district today loses it: FL, MS, SC, TN.
Two different stories sit inside that one chart. In Alabama and
Louisiana the neutral maps rarely produce a Black-plurality district on
their own, so those seats exist because a judge required them. In
Georgia the Black population is numerous and concentrated enough that
neutral maps produce such districts most of the time, and a maximized
gerrymander still cuts 4 down to 2. Concentration protects a group from
accidental erasure. It does not protect them from a map drawn on
purpose.
Kenny and colleagues (2026) run the harder version of this, with a
real seat-maximizing search across all fifty states, and reach the same
shape of answer.
What this brief cannot tell you
The neutral maps followed three rules, and a real map has to
follow more. Federal law adds two hard ones: near-exact equal
population between congressional districts, which the simulations
honoured, and the Voting Rights Act’s limits on how lines may treat
racial minorities, which they never considered. Everything else is state
law and differs by state. Many states require respect for county and
city boundaries, or for communities of interest, or for the cores of
prior districts. That last rule protects incumbents by protecting the
shape they were elected in.
Those criteria conflict, and few states rank them. A state can point
at a neutral map and say it split a county the state’s own constitution
protects, and the state would be right. It does not follow that the gaps
in Figures 1 and 2 are explained by county lines, and nothing here
measures how much of each gap the extra rules could account for.
That objection now has legal force. In Louisiana
v. Callais (2026) the Supreme Court held that a map offered to show
what could have been drawn must meet all of the state’s legitimate
objectives, its stated political goals included. Nothing in a 5,000-map
ensemble built on three rules can clear that.
Two smaller limits. Party control of a legislature is a rough proxy
for who drew a map, and for at least three of the 20 states in Figure 3
it is the wrong answer. Iowa’s maps are drafted by nonpartisan staff,
Utah had an advisory commission, and Ohio’s process is a hybrid. Every
count here is also a snapshot of maps and law that both keep moving.
What you should have learned
- A map’s shape is not evidence, and its position in a distribution of
maps is. That is the whole move: build the plans nobody had a reason to
draw, then locate the real one among them.
- Neutral maps produce about 1.38 times as many competitive districts
as the enacted maps do, 108.8 against 79 within five points of even, and
the result survives every threshold checked.
- The national gap is concentrated, not spread: Texas alone runs 2
competitive districts against a neutral average of 8.7.
- A commission is not a machine for producing the neutral map.
Commission states mostly sit close to their ensembles, and California,
drawn by a commission, sits third in the country for distance from its
own.
- Under the most adversarial map the simulations contain,
Black-plurality districts in the 20 states fall from 14 to 2, and only
Georgia keeps any.
Extensions
None of these is answered above, and every one can be answered from
the tables the Sources section hands over.
competitive_by_state.csv puts enacted
against neutral_mean for every state. Sort by the
difference. Which maps sit furthest from what a neutral process
produces, and in which direction?competitive_national.csv repeats the comparison at four
values of threshold. Does the conclusion survive changing
what counts as competitive?black_by_state.csv compares actual_black
against neutral_black_mean. Find the states whose enacted
map produces more than neutrality would, and the states where it
produces fewer.who_draws_states.csv gives each state its
congressional_authority. Match it to the gap in
competitive_by_state.csv. Do commission states really look
different?- Stretch.
black_by_state.csv also has
n_plans_tied_at_max. Where that number is in the thousands,
the state’s highest Republican seat count is easy to reach. Ask what
that implies about how much skill a gerrymander takes.
- Stretch. The ALARM collection is rebuilt as states
redraw. Download a state that has enacted a new map since this snapshot
and see whether its position in the ensemble moved.
Sources
Data
The data itself
Every figure above is drawn from these tables. They are plain CSV,
they open in a spreadsheet, and they are yours to take further.
black_by_state.csv,
black_national.csv,
competitive_by_state.csv,
competitive_national.csv,
who_draws.csv, who_draws_states.csv
One more file is not data about the subject – it is how this chapter
checked its own numbers: facts.csv, the individual
numbers the text above quotes.
Cases
Academic literature
- McCartan, C. and Imai, K. (2023). “Sequential Monte Carlo for
Sampling Balanced and Compact Redistricting Plans.” The Annals of
Applied Statistics 17(4): 3300–3323. The algorithm behind the 5,000
maps. https://doi.org/10.1214/23-AOAS1763
- Kenny, C. T., Zhou, B., Simko, T., and Imai, K. (2026). “Weakening
the Voting Rights Act Reduces Minority Representation and Electoral
Competition.” Working paper. A more thoroughly optimized version of this
brief’s second question, run across all 50 states with a genuine
seat-maximizing search rather than a best-of-5,000 selection. Its
published estimate is a national decline of roughly half in
minority-opportunity districts. https://imai.fas.harvard.edu/research/callais/
Rebuild this data yourself, with an AI assistant
I want to rebuild a public dataset from its original source, without
any starting files. Please do the following and show your work.
THE SOURCE. The ALARM Project's 50-State Redistricting Simulations,
on the Harvard Dataverse: doi:10.7910/DVN/SLCD3E. For every state
with more than one congressional district, it holds a table with one
row per district per redistricting plan. Query the Dataverse API for
the file list, then download each state's "<STATE>_cd_2020_stats.tab"
file with ?format=original appended to the access URL, which returns
the original CSV rather than Dataverse's re-encoded copy. Forty-four
states qualify; the six single-district states (Alaska, Delaware,
North Dakota, South Dakota, Vermont, Wyoming) are not in the file at
all, because a state with one district has nothing to simulate.
Each file is 7 to 18 MB, so do not commit the raw downloads -- pull
them into a temporary folder, compute what you need, and keep only
the small summary tables.
The `draw` column tells you which plan each row belongs to:
"cd_2020" is the map the state actually enacted after the 2020
census; the 5,000 draws numbered 1 through 5000 are computer-drawn
plans, built to the same population-equality, contiguity, and
compactness rules, with no information about party or race.
WHAT TO BUILD.
1. COMPETITIVENESS. For each state and each of four thresholds
(2.5, 5, 7.5, 10 percentage points), count the districts within
that many points of a 50-50 two-party vote share (columns ndv and
nrv) in the enacted plan, and average the same count across the
5,000 neutral plans.
2. BLACK REPRESENTATION UNDER A MAXIMIZED GERRYMANDER. Restricted to
the 20 states Republicans controlled after the 2020 census (TX,
FL, GA, NC, SC, TN, AL, MS, LA, AR, MO, KS, OK, IA, NE, IN, OH,
KY, WV, UT). A district is "Black-plurality" if Black voting-age
population is the largest of all eight reported VAP columns
(vap_white, vap_black, vap_hisp, vap_aian, vap_asian, vap_nhpi,
vap_other, vap_two) -- not merely larger than white VAP alone.
For each state, report the enacted count, the mean across the
5,000 neutral plans, and -- among whichever plans are tied for
that state's highest Republican-seat count -- the fewest
Black-plurality districts found among them.
A note on staleness: the enacted ("cd_2020") plan in this dataset
predates two court-ordered maps that added a second Black-opportunity
district for the 2024 election onward, in Alabama (Allen v. Milligan,
2023) and Louisiana (Robinson v. Ardoin, 2024 -- the same map
Louisiana v. Callais later ruled on in 2026). If you want the current
picture rather than the file's own snapshot, add one seat to each of
those two states' enacted counts by hand, and say that you did.
CHECK YOUR WORK. The copy this book used was downloaded in August 2026.
If your rebuild matches it, across the 44 states (429 districts) you
should find:
- 79 districts competitive within 5 points in the enacted maps,
against a mean of 108.8 across the neutral plans
- Texas: 2 competitive districts enacted, 8.7 expected under neutral
maps -- the largest gap of any state
Restricted to the 20 Republican-controlled states (191 districts),
with the Alabama/Louisiana correction applied:
- 14 Black-plurality districts enacted, a mean of 5.3 under neutral
maps, and 2 under a maximized gerrymander
- Georgia is the only one of the 20 that keeps any Black-plurality
district under the maximized gerrymander (4 enacted, 2 remaining)
