Gerrymandering: Turning District Shape Into Election Outcome

Same votes, different map, different winner

Redistricting is unavoidable in any system that elects representatives from geographic districts rather than at large — someone has to draw the lines. The uncomfortable fact underlying gerrymandering is that, for a fixed set of voters and votes, the choice of where to draw those lines can single-handedly flip which party wins a majority of seats, without changing a single person's vote. The term dates to 1812, when a Massachusetts district drawn to favour Governor Elbridge Gerry's party was said to resemble a salamander — the "Gerry-mander."

Two techniques: packing and cracking

There are two complementary ways to distort a map, and skilled gerrymanders typically use both at once. Packing draws a small number of districts that concentrate the opposing party's supporters into overwhelming, wasteful majorities — a district the opposition wins 90-10 "wastes" nearly 40 percentage points of votes beyond what was needed to win it. Cracking does the opposite: it splits the opposing party's voters thinly across many districts, so they form a minority everywhere and win nowhere, wasting every one of those votes on the losing side. Every packed district frees up a surplus of favourable voters that can then be spread — cracked — across several more districts to secure them too.

wasted votes for a party in one district:
  if the party LOSES the district → all of its votes are wasted
  if the party WINS the district  → votes beyond the bare majority
                                     needed to win are wasted

packing:  push opposition wasted votes UP (win them 90-10 instead of 55-45)
cracking: push opposition wasted votes UP the other way
          (make them lose 45-55 in many districts instead of winning few)

efficiency gap = (wasted_A − wasted_B) / total votes cast

Measuring distortion: the efficiency gap

Because packing and cracking both work by manipulating wasted votes, political scientists Nicholas Stephanopoulos and Eric McGhee proposed in 2015 measuring exactly that: sum every wasted vote for each party across all districts in a plan, take the difference between the two parties' totals, and divide by the total votes cast. A large efficiency gap in one party's favour is the statistical signature packing and cracking leave behind — the party benefiting from the map keeps winning seats with comparatively little vote-margin waste, while the other party's votes are wasted disproportionately, whether through lopsided losses or lopsided overwhelming wins. It is not the only diagnostic tool in use — researchers also compute the mean-median difference and simulate large ensembles of algorithmically generated alternative maps to see whether the enacted plan is a statistical outlier — but the efficiency gap remains one of the most widely cited single-number summaries.

Shape as a clue, not proof

Bizarre, tentacled district shapes are the popular image of gerrymandering, and compactness measures such as the Polsby-Popper score (comparing a district's area to the area of a circle with the same perimeter) are used to flag unusually contorted boundaries. But shape alone is an imperfect signal: some naturally occurring, geographically constrained districts are irregular for entirely legitimate reasons — following a coastline, a river, or dense urban clustering — while other maps with reasonably compact-looking districts can still be highly partisan if the underlying population is unevenly distributed. This is why efficiency-gap-style vote-outcome metrics and shape-based compactness metrics are typically used together rather than in isolation.

Where the courts stand

The U.S. Supreme Court's 2019 decision in Rucho v. Common Cause held that partisan-gerrymandering claims present a nonjusticiable political question that federal courts cannot resolve, closing off one major avenue of legal challenge at the national level — a case that followed years of litigation, including Gill v. Whitford, in which the efficiency gap itself was presented as evidence. Racial gerrymandering remains subject to federal review under the Voting Rights Act and the Constitution's equal protection guarantee, and several state courts have since struck down partisan gerrymanders under their own state constitutions, leaving the practical fight over partisan district-drawing largely to the states.

Frequently asked questions

Try it live

Everything above runs in your browser — open Gerrymandering Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.