SalamanderThe Lab
How do you measure a rigged map?
Courts, researchers and reform commissions use a handful of yardsticks. Here are three you can play with: wasted votes, compactness, and the smallest share of the vote that can still win a majority of seats.
1 · The wasted-vote calculator
A vote is wasted if it didn't help elect anyone: every vote for a losing candidate, and every vote for a winner beyond the bare majority they needed. Packing wastes the other side's votes in landslides. Cracking wastes them in narrow defeats.
The efficiency gap, proposed by law professor Nicholas Stephanopoulos and political scientist Eric McGhee, is the difference between the two parties' wasted votes divided by all votes cast. In the Wisconsin case Whitford v. Gill, a district court weighed an efficiency gap of about 11.7% to 13% for the state's Assembly map. (The Supreme Court later sent that case back on standing, and in 2019 ruled that federal courts can't police partisan gerrymanders at all.)
gap = (wasted Plum − wasted Peach) ÷ total votes
Five districts of 100 voters each. Drag the sliders to set Plum's share in each district, or try a preset.
Solid = votes that elected someone. Striped = wasted votes. ● Plum · ▲ Peach.
2 · Be the judge: score a district's shape
Click or drag to paint one district. Salamander uses the Polsby–Popper test: compare the district's area with the area of a circle that has the same perimeter. Long arms, tails and holes raise the perimeter, and the score falls. On a grid a square is the best possible shape, so we scale the score to make a square 100.
The judge is waiting.
3 · How small a minority can win?
To win a majority of seats you only need a bare majority in a bare majority of districts, and nothing anywhere else. With equal-sized districts, the smallest vote share that can win is roughly half of a half: 25%. Real maps never get close, because voters aren't pieces you can place one at a time, but the maths shows why lines matter so much.
4 · The hall of infamous shapes
Real districts that became famous for their shapes.