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Topic: Districting — when the lines decide, and no method can undo them

Topic hub — a cross-method view. Every voting method on this site answers one question: given these ballots, who wins? Districting asks something no method controls — who gets grouped with whom before any counting starts. Split one electorate into several, elect a winner in each, and the aggregate result becomes a function of where the lines fall, not only of how people voted.

The one idea to take away: districting is a pre-tabulation choice, and a better count cannot reverse it. STAR, Ranked Robin, Approval and IRV can all be perfectly correct inside every district and still produce an aggregate nobody would have chosen. The failure is upstream of the tabulator, which is exactly why it survives every reform that only changes the count.

Level: 201 → 301 · for debaters

The distinction that keeps getting muddled: districting vs. summability

These look identical — both split ballots into geographic pieces — and they are opposite questions.

Summability Districting (this hub)
The question can precinct subtotals be added to recover the one true winner? each district elects its own winner; what does the aggregate mean?
The pieces are an implementation detail — merged before anyone is elected the actual constituencies — never merged
It's a property of the count (STAR ✅, Ranked Robin ✅, IRV ❌) the architecture — no method is immune
Fixed by choosing a summable method only by changing the districts, or electing more than one per district

So "our method is summable" answers the auditing question and says nothing about the districting question. Keep them apart in an argument; conflating them concedes a point you didn't have to.

Where each piece is treated

The idea What it says Page
The theory what the architecture costs, measured with the same instrument as distortion: counting by district has a price you can bound Distributed voting — the price of counting by district (301)
The paradox reinforcement / inconsistency: two districts each elect X, the merged electorate elects someone else. Additive rules (Score, Approval, Plurality) are immune by arithmetic; STAR, Ranked Robin and IRV are not The multiple-districts paradox
The cost, counted Ana is adored in Northside, Beto in Southside, Cleo is everybody's solid second — and Cleo wins no district at all while being the best choice overall The districting cost
The reversal, counted both halves pick Ada; the whole picks Cara. At ≥ 8 voters no Condorcet method can avoid it Reinforcement paradox
The elimination version B wins both districts and is eliminated when they merge — the IRV-specific shape of the same problem IRV isn't summable · summability demo
Seats vs. votes over half the seats on under half the votes — and why "that's just gerrymandering" is the wrong diagnosis False majorities (201)
The law "one person, one vote" as the courts mean it is a districting rule (Reynolds v. Sims, Wesberry) — settled, and every method here clears it One person, one vote
The structural answer multi-member districts with proportional seats: fewer lines to draw, and far harder to draw for advantage Proportional STAR · Electing more than one
The downstream effects wasted votes, packing and cracking, and the two-party equilibrium single-member lines produce Wasted votes · Two-party dominance
Try it yourself a city whose two districts each run their own count, and what the merge does Two districts, one mayor (ex01)

Reading it fairly

Three cautions, because this topic invites overclaiming in both directions.

Against overclaiming for reform: single-member districts are not made unfair by gerrymandering — the structural distortion is there in fairly drawn lines too, which is a stronger argument and a more honest one. But the mirror error is just as common: a better ballot does not fix districting, and no page here should imply it does. STAR in every district is still one winner per district.

Against overclaiming against districts: the published experiments cut both ways. On real-world preference data the measured cost of counting by district is much smaller than the worst case — real electorates are comparatively homogeneous, and homogeneity is what saves you. Quote the worst case as a worst case, per reading these fairly.

And keep the vocabulary straight. Reinforcement (a.k.a. consistency / join-consistency) is the criterion; the multiple-districts paradox is its failure; gerrymandering is the deliberate manipulation of where lines fall; malapportionment is districts of unequal population, which is the thing the law actually forbids. They are four different claims and only one of them is illegal. → glossary

See also