District boundaries

Why can the drawing of district lines settle an election before any vote is cast?

We treat the count as the thing that decides an election. But under single-member districts the votes are not counted once — they are counted separately inside boundaries someone drew beforehand. So here is the question worth sitting with: if every vote in a territory were fixed in advance, how much freedom would the mapmaker still have over the result?

Let us make it small enough to check by hand. A territory of 100 voters, five districts of 20 each, one seat per district on a simple majority — so 11 votes takes a seat. Party A has 60 supporters, party B has 40. Those totals never change; only the lines do.

Map one. Spread B's voters evenly: every district holds 12 A and 8 B. A wins all five. Sixty per cent of the vote, all of the seats.

Map two. Concentrate B: two districts of 18 B and 2 A, then the remaining sixty voters — 56 A and 4 B — split 19/1, 19/1 and 18/2. B wins two, A wins three, which is exactly A's 60 per cent.

Map three. Now let B draw. B has only 40 voters but needs just 11 per district, so three districts of 11 B and 9 A give B three seats. That uses 33 of B's voters and 27 of A's, leaving 7 B and 33 A for the last two — say one of 20 A, and one of 13 A with 7 B, both won by A. Final: B takes three seats of five with 40 per cent of the vote.

The totals are 60 and 40 in all three. The same voters, living in the same places, yield A five seats, three, or two — and no fraud occurred anywhere in it.

What were the two moves? Map three used them both. Packing puts an opponent's voters into a few districts they win overwhelmingly, so the surplus elects nobody. Cracking splits the rest across districts where they are a permanent minority, so those votes elect nobody either. Every vote above the number needed to win, and every vote cast in a district lost, buys nothing. A mapmaker is not adding votes to their own side; they are arranging for the other side's votes to be spent wastefully.

That suggests a measure, and the efficiency gap is the best-known attempt at one. Count each party's wasted votes — surplus above the winning threshold in seats it won, plus everything cast in seats it lost — take the difference and divide by total votes. In map one, A wastes 1 per district and B wastes 8, so the gap is (40 - 5) / 100, or 35 points in A's favour. In map three it runs the other way: A wastes 38, B wastes 7, a gap of 31 points favouring B. The numbers do capture what our eyes saw.

But the objections are real. The measure builds in a particular assumed relationship between vote share and seat share, so a map can score badly for reasons the mapmaker did not create. It is unstable: a modest swing can move a district from one column to the other and flip the sign, so one election's figure is weak evidence about intent. It counts a surplus in a safe seat as waste, penalising support that is naturally concentrated. And in Rucho v. Common Cause in 2019 the US Supreme Court held partisan gerrymandering claims non-justiciable in federal courts on the ground that no such standard is judicially manageable — so it remains an analytical tool, not a legal test.

Then the complication that most deserves stating plainly: some packing happens with nobody intending it. Voters are not distributed at random. In many countries one party's support is concentrated in dense urban areas where it wins by enormous margins, while the other's is spread thinly across suburbs and countryside — and compact, contiguous, entirely innocent districts drawn over that geography will pack the urban party by accident. Chen and Rodden's work on simulated neutral maps is the standard demonstration. So an unequal seats-to-votes outcome is not by itself proof of manipulation; you have to compare the real map against what neutral maps of the same territory produce.

Three refinements worth keeping.

First, this is a property of single-member districts as such, not evidence of wrongdoing in any particular case. Any winner-take-all division converts votes into seats non-proportionally; drawing the lines merely chooses which distortion.

Second, distinguish the map from the intent. The same seat outcome can come from deliberate packing, from innocent compactness over clustered voters, or from both — and the honest way to tell them apart is comparison against a large ensemble of neutrally generated maps, not inspection of a district's shape. Odd shapes are suggestive and nothing more; some are required by rivers, coastlines or rules protecting minority representation.

Third, the criteria pull against each other. Compactness, respect for municipal boundaries, competitiveness, proportionality, and districts in which a minority group can elect its preferred candidate cannot all be maximised at once. A commission choosing among them makes a contested value judgement rather than applying a neutral rule — which is why "just draw fair districts" is an instruction with no single meaning.

• How ensembles of computer-generated neutral maps are used to test a real map for partisan bias.
• Why proportional and mixed-member systems relocate rather than remove the boundary-drawing problem.

Every term the collection defines is gathered in the glossary.