The Efficiency Gap: Why a Single Number Can Prove That a Legislative Map Is an Unconstitutional Gerrymander

Consider a hypothetical state of exactly 500 voters, divided into five legislative districts of 100 people each. If Party A and Party B each have 250 supporters, a perfectly representative map would yield a legislature split three to two. But if Party A controls the mapmaking, they can pack 85 of Party B's voters into a single district, and spread the remaining 165 across the other four districts in 47-vote minorities. Party A wins four seats to one, securing 80 percent of the legislature with only 50 percent of the statewide vote. This is the mathematical engine of partisan gerrymandering, and for decades, the United States Supreme Court refused to strike down such maps because no one could provide a single, objective number to prove when the political gamesmanship became unconstitutional. That changed when legal scholar Nicholas Stephanopoulos and political scientist Eric McGhee introduced a metric designed to quantify that exact distortion: the efficiency gap.[1][6]

The efficiency gap is an argument that fairness in a two-party electoral system can be measured by counting the votes that do not matter. In any single-member district election, votes cast for a losing candidate are mathematically wasted, as are any surplus votes cast for a winning candidate beyond the 50 percent plus one needed to secure the seat. According to PlanScore, a nonpartisan redistricting tracker, the metric is defined simply: "The efficiency gap is calculated by taking one party's total inefficient votes in an election, subtracting the other party's total inefficient votes, and dividing by the total number of votes cast." The resulting percentage represents the structural advantage one party holds over the other.[5]

To understand the calculation, consider a district where 100,000 votes are cast. A candidate needs 50,001 votes to win. If the Democratic candidate receives 75,000 votes and the Republican receives 25,000, the Republican has 25,000 lost wasted votes. The Democrat has 24,999 surplus wasted votes—the votes above the 50,001 threshold. In this single district, the wasted votes are nearly identical, meaning the district itself is highly efficient and unbiased. But gerrymandering is a statewide exercise. Mapmakers do not look at single districts; they look at the aggregate.[1][6]

The power of the efficiency gap lies in its direct targeting of the two primary tactics of gerrymandering: 'packing' and 'cracking.' Packing concentrates the opposing party's voters into a few districts where they win by massive margins—say, 90,000 to 10,000. This generates 39,999 surplus wasted votes for the packed party. Cracking dilutes the remaining opposing voters across multiple districts where they lose by narrow margins—say, 48,000 to 52,000. This generates 48,000 lost wasted votes per district. By capturing both tactics in a single equation, the efficiency gap provided the courts with the manageable standard they had been demanding since the 1980s.[1][5]

In their 2015 paper published in the University of Chicago Law Review, Stephanopoulos and McGhee did not just propose the formula; they proposed a specific legal threshold. After analyzing decades of congressional and state legislative elections, they argued that an efficiency gap of 8 percent in state legislative races, or two seats in congressional races, should trigger a presumption of unconstitutionality. Above that threshold, they found, the structural advantage becomes so entrenched that the favored party is virtually guaranteed to maintain control of the chamber for the entire decade the map is in effect, regardless of normal shifts in voter preference.[1]

The metric quickly moved from academic journals to federal courtrooms. In 2016, a federal district court used the efficiency gap to strike down the Wisconsin State Assembly map. The court noted that in 2012, Republicans won 60 of the 99 Assembly seats with only 48.6 percent of the statewide two-party vote. The plaintiffs used the efficiency gap to prove this was not a geographic accident; the map produced an efficiency gap of between 11.69 percent and 13 percent in favor of Republicans. It was the first time in American history a federal court had invalidated a redistricting plan purely on the grounds of partisan gerrymandering.[1][6]

When the case, Gill v. Whitford, reached the Supreme Court in October 2017, the efficiency gap was the centerpiece of the oral arguments. The justices debated it as the potential holy grail of redistricting law, though some expressed deep skepticism. Chief Justice John Roberts famously dismissed the sociological metrics as 'sociological gobbledygook,' expressing concern that the Court would be forced to evaluate complex mathematical formulas in every election dispute. Yet, the fact that the Court was debating a specific algebraic formula at all represented a seismic shift in election law.[4]

However, the metric is not without its critics, and the argument that a single number can define democratic fairness faces significant mathematical and legal pushback. As detailed in a Yale Law Journal evaluation, the efficiency gap makes a fundamental assumption about competitive elections: it assumes that proportional representation—where a party's seat share matches its vote share—is the baseline of fairness. But the United States uses a winner-take-all, single-member district system, which naturally awards a 'winner's bonus' to the majority party. Critics argue that penalizing a map for failing to achieve proportional representation attempts to rewrite the rules of American elections through a mathematical backdoor.[2]

Furthermore, the efficiency gap struggles with the reality of political geography. In many states, Democratic voters are heavily concentrated in dense urban centers, while Republican voters are spread more efficiently across vast rural and suburban areas. This natural clustering means that Democrats will often win urban districts by 80 or 90 percent, generating massive numbers of surplus wasted votes without any intentional gerrymandering by the opposing party. A paper published on the arXiv preprint server highlighted this geographic penalty, noting that applying the efficiency gap strictly could force mapmakers to draw bizarrely shaped districts just to unpack urban voters and balance the wasted vote totals.[3]

Eric McGhee himself addressed some of these misconceptions in a 2017 piece for The Washington Post, clarifying that the efficiency gap was never intended to mandate strict proportional representation. He noted that the metric actually allows for a winner's bonus, provided that the bonus is symmetric. In a symmetric system, a party that wins 55 percent of the vote might win 65 percent of the seats, but if the other party wins 55 percent of the vote in the next cycle, they too would win 65 percent of the seats. The goal is not to eliminate wasted votes, but to ensure that the map does not structurally condemn one party to waste significantly more votes than the other regardless of the electoral environment.[4]

Today, platforms like PlanScore use the efficiency gap alongside other metrics like partisan bias and the mean-median difference to evaluate the fairness of maps across the country in real-time. By feeding proposed maps into these scoring systems, transparency advocates can instantly quantify the partisan skew of a legislative boundary before it is even voted into law. PlanScore's historical data shows that the efficiency gap of congressional maps spiked significantly after the 2010 redistricting cycle, when advanced mapping software allowed mapmakers to pack and crack with unprecedented precision.[5]

While the Supreme Court ultimately sidestepped the core constitutional question in the Wisconsin case and later ruled in 2019 that federal courts cannot hear partisan gerrymandering claims, the efficiency gap did not disappear. Instead, the legal battleground shifted to state supreme courts. Operating under their own state constitutions—many of which contain explicit guarantees of 'free and equal' elections—state judges continue to rely on the metric to quantify the severity of partisan distortions. In states like Pennsylvania and North Carolina, the efficiency gap has been cited in rulings that forced the redrawing of heavily skewed maps.[6]

The next major test for the efficiency gap will arrive with the 2030 redistricting cycle. As state legislatures prepare to draw new maps using the 2030 census data, the metric's survival depends entirely on state supreme courts. If conservative-leaning state courts follow the federal judiciary's lead and declare partisan gerrymandering a non-justiciable political question, the efficiency gap will be reduced to an academic exercise in those jurisdictions. But in states where courts remain willing to intervene, mapmakers will be forced to run their proposed boundaries through the Stephanopoulos and McGhee formula before a single vote is cast, ensuring that the math of wasted votes dictates the shape of the legislature.[6]