Gerrymandering by the Numbers: What the Efficiency Gap Shows

Few words in American politics carry as much heat as "gerrymandering." With several states, led by both parties, having considered or enacted new congressional maps in the middle of the decade (Voting Rights Lab), the term is everywhere again. This article takes no side. It explains how statisticians try to measure what maps do to votes and seats, and what those measures can and cannot prove.

Packing, cracking and wasted votes

Two tactics sit at the center of the debate. Packing crams one party's voters into a few districts that they win by huge margins. Cracking splits them across several districts where they narrowly lose. Both leave the targeted party with many "wasted" votes: every vote for a losing candidate, plus every vote above what the winner needed.

The efficiency gap in four districts

The efficiency gap, proposed by Nicholas Stephanopoulos and Eric McGhee, is the difference between the parties' wasted votes divided by the total votes cast (Stephanopoulos and McGhee, 2015).

Take four districts of 100 voters each, with Party A and Party B each receiving 200 votes in total. In Map X, A wins one district 85-15, and B wins the other three, 60-40, 60-40 and 65-35. Party A wastes 149 votes and Party B only 47, so the gap is (149 − 47) / 400, about 25%, in B's favor, though votes split evenly.

In Map Y, each party wins two districts 55-45, and each wastes 98 votes. The gap is zero. The scientific calculator handles this arithmetic.

One map is not enough

Before concluding anything from four districts, consider chance. If each district were a pure toss-up, the binomial distribution calculator shows that Party A would win one seat or fewer about 31% of the time. A lopsided split can arise without any design.

That is why serious analyses look at many districts and many elections, and why the authors proposed thresholds, around 7% to 8%, before calling a plan an outlier (Brennan Center). Any such threshold is a convention, not a law of nature, and experts dispute where to draw it.

A single election can make an innocent map look skewed, or a skewed map look innocent.

Comparing with thousands of maps

Another approach has a computer draw thousands of legal maps and checks where the enacted plan falls among them. One scholar said of Wisconsin that virtually none of the computer-produced maps were as uncompetitive as the enacted plan (Daily Cardinal). The method asks a different question from the efficiency gap: not how many votes were wasted, but whether typical maps drawn under the same rules would produce this outcome.

Both approaches have limits. The efficiency gap shifts when voters swing, and geography matters, since clustered supporters can end up with fewer seats than votes under neutral lines. The descriptive statistics calculator summarizes district margins.

What courts and numbers cannot settle

In 2019 the Supreme Court held 5-4 that partisan gerrymandering claims present political questions beyond the reach of federal courts, in a ruling that combined a challenge to a North Carolina map drawn by one party with a challenge to a Maryland map drawn by the other (Faegre Drinker summary).

Measurements inform the debate, but whether a given gap is acceptable is a question of law and politics, not statistics.