2Federal redistricting

Districts a clerk can check with a ruler.

  • Equal population: each congressional district contains substantially the same number of people.
  • The ruler test: a straight line may pass through the district once, not leave and re-enter.
  • The 3-to-1 test: no district may be more than three times as long as it is wide.
Diagram · the ruler tests
Passes · the line crosses twice
Fails · the line crosses six times

The system.

Gerrymandering is usually attacked on intent, which is exactly the wrong surface. Intent is invisible, arguable, and litigated for a decade. Shape is visible on day one. The maps that offend people are the ones that look wrong, and they look wrong because a mapmaker had to reach across a metro area to grab a neighborhood.

The incentives.

When a legislator picks their voters, the general election stops mattering and the primary becomes the whole contest. That rewards the candidate who is most unyielding rather than the one who is most representative, in both parties, structurally. A district that has to be a compact place is a district that has to contain people who disagree with each other.

The constraints.

Both tests are geometry, not policy, which is the entire point. The convexity test (a ruler crosses the boundary exactly twice) kills the tendrils and the barbells. The skinniness test (no dimension greater than three times the perpendicular one) kills the snakes along a highway. A clerk can check them. A judge can verify them. A lobbyist cannot argue them into ambiguity.

Where I'm still wrong.

Geography is stubborn — coastlines, rivers, mountain ranges and state borders will sometimes make a perfect score impossible. I would rather write a narrow, explicit exception for natural boundaries than soften the rule into a vibe. Where exactly that exception starts is a real open question, and it is the one place a special interest will try to live.

Steelman · § 2

The strongest objection.

Compactness is not politically neutral, even though the test is. Democratic voters cluster densely in cities, so tidy, compact districts tend to pack them together and produce a modest Republican-leaning skew — nobody's intent, just geography meeting geometry. That is a genuine cost of choosing a rule you can check with a ruler over a rule that targets outcomes. My answer is that a small, visible, geographic skew is a better problem than an invisible, deliberate, litigated one — and that the geometry should be paired with a second rule: mapmakers may not use partisan registration or incumbent addresses as inputs at all.

Specification · § 2

The test, in full

The test does not ask whether a district is fair. It asks a narrower question that a nonexpert can answer while looking at the same map: does this shape pass three simple rules?

Rule 1Equal population

A district must contain substantially the same number of people as every other district in the same plan, using the population-equality standards already required by law.

Divide the district population by the ideal district population and report the deviation as a percentage. Ideal 100,000 against an actual 101,000 is +1%. This is reported separately from the geometric tests, and it uses population only — never party, election results, race, income, or religion.

Rule 2The ruler test

A straight line may pass through a district once. It may not leave the district and then enter the district again.

For any straight line drawn across the map, the portions of that line lying inside the district must form one continuous segment. A district fails if any line produces the pattern: inside → outside → inside. Squares, rectangles, triangles, circles, trapezoids and other simple convex shapes pass. C-shapes, U-shapes, hooks, dumbbells, deep inward notches, districts that wrap around another district, and long corridors that bend around territory and reconnect all ordinarily fail. When a district fails, the readout shows at least one line that enters, leaves, and enters again.

RULER TEST: PASS / FAIL

Rule 3The 3-to-1 test

No district may be more than three times as long as it is wide. This is what stops a district that passes the ruler test from simply being drawn as an extremely long, narrow strip.

Find the smallest rectangle that contains the district, free to rotate to whatever orientation fits best, and divide its long side by its short side. 1:1, 2:1 and 3:1 pass. 3.1:1 and 6:1 fail. Report both the ratio and the result: “Length-to-width ratio: 2.4:1 — 3-TO-1 TEST: PASS.”

3-TO-1 TEST: PASS / FAIL

ClarificationThe map may bend because the world bends

Real boundaries follow permanent physical features — roads, railroads, rivers, bayous, coastlines — and those features curve. Ordinary bends in a river should not fail a district.

So for testing purposes only, a continuous stretch of boundary that follows a qualifying physical feature is treated as the straight segment connecting its two endpoints. If the boundary follows a winding bayou from A to B, the real boundary remains the bayou; the test simply substitutes the straight line from A to B. A feature qualifies only if all of the following hold:

  • It appeared on an official geographic map before the redistricting process began.
  • The district follows one continuous feature between the two endpoints.
  • The feature does not double back between those endpoints — it may meander while generally progressing from A toward B, but it may not reverse substantially, loop around territory, and return.

How a district is evaluated.

  1. 1.Identify the portions of the boundary that follow qualifying permanent physical features.
  2. 2.Replace each qualifying curved portion with the straight segment joining its endpoints — for geometric testing only.
  3. 3.Apply the ruler test to the resulting simplified shape.
  4. 4.Find the best-fitting enclosing rectangle and compute its long-to-short ratio.
  5. 5.Separately, compare district population with the ideal district population.

The readout.

POPULATIONPass / Fail
RULER TESTPass / Fail
3-TO-1 TESTPass / Fail
OVERALLPass / Fail
The map may bend because the world bends. It may not bend simply because the mapmaker wants it to.

The test deliberately cannot tell you whether Republicans or Democrats benefit, whether the district is competitive, what its racial or economic composition is, whether the statewide result is proportional, or what the mapmaker intended. It evaluates geometry and population, and nothing else. A district fails overall if it fails any one rule.

Discussion

Tell me where this is wrong.

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