To say there is an "efficiency gap" between two people is a wonky way of claiming one person is more productive than another at work. Perhaps one has an advantage of better tools.
That's essentially what's being measured by a new mathematical formula that calculates the "efficiency gap" between political parties in elections. The formula determines which party is more efficient at translating votes into victories, and it's being cited in a high-profile court case from Wisconsin to help measure whether political gerrymandering gives one party an unfair advantage.
Since its creation a few years ago, the efficiency gap has been embraced as "corroborative evidence" by a federal appeals court panel that ruled that Wisconsin Republicans intentionally drew district boundaries for the state Assembly to the disadvantage of Democrats.
The U.S. Supreme Court has agreed to hear arguments on that case. If upheld, it could set a nationwide precedent for determining when partisan gerrymandering crosses the line into an unconstitutional infringement on voters' rights to representation.
The Associated Press used a version of the efficiency gap formula — developed by University of Chicago law professor Nick Stephanopoulos and researcher Eric McGhee of the nonpartisan Public Policy Institute of California — to analyze the results of the 2016 U.S. House and state House or Assembly elections.
Which races were excluded?
U.S. Senate elections were excluded, because they are held on a statewide basis, so gerrymandering would not apply. State senate elections and North Dakota House elections also were excluded, because they do not happen all at once, and thus the results would span multiple elections.
Following the researchers' methodology, the AP looked only at votes cast for Republicans and Democrats, because independent and third-party candidates receive a relatively small portion of the overall vote.
This meant a few state house districts — one in Rhode Island, two each in Alaska and Maine, and seven in Vermont — were excluded from the analysis, because they were won by independents. Nebraska's state legislative elections were left out because all candidates run on a non-partisan basis.
How does it work?
For all other races, the AP figured the share of the vote received by each party in each district. It then calculated each party's district average vote share in a state. And it compared that to the share of seats won by each party.
In Michigan, for example, Republican state House candidates received a total of 2,263,633 votes statewide, about 3,000 more than Democrats. But those virtually similar totals were not split evenly among districts.
Republicans received a district average of a little over 48 percent of the vote compared with nearly 52 percent for Democrats; yet the GOP won 57 percent of the House seats compared with just 43 percent for Democrats. The upshot: Republicans won more often, even though Democrats had larger victory margins.
One possible explanation is that gerrymandering packed Democratic voters into a concentrated number of state House districts, which limited their ability to elect a larger number of representatives.
The efficiency gap measures "wasted votes," defined as all those cast for a losing candidate, as well as any votes for the winner beyond what was needed to win.
In Michigan, the formula shows Republicans "wasted" 19.8 percent of their votes while Democrats "wasted" 30.2 percent. The difference results in a 10.3 percent "efficiency gap" in favor of Republicans.
Put another way, Michigan House Republicans won about 10 percent more seats than would normally have been expected, based on their district average vote share — an indication that district boundaries were more favorable to Republicans.
Michigan provides a simple case, because both major parties fielded candidates in all state and U.S. House races. But in many states, at least some candidates faced no major-party opposition.
Political scientists say it is unreasonable to assume that 100 percent of voters favor one particular party. So for uncontested races, experts typically estimate how voters might have acted if they had choices.
They often derive those figures based on how a party's presidential candidate fared in legislative districts, whether those legislative races featured incumbents and how the parties fared in those districts in previous contested races. But 2016 presidential vote shares aren't yet available nationwide on a state House district level.
As an alternative, the AP substituted a 75-to-25 vote share for uncontested races in its analysis. That essentially held each party's "wasted votes" neutral in those districts. Stephanopoulos said it's a reasonable approach, although the actual magnitude of a state's efficiency gap could be even greater than the AP's figures if there were a lot of uncontested races.
A gerrymander threshold
There is no definitive answer to the question of how large an efficiency gap must be to suggest an unconstitutional gerrymander.
In the Wisconsin case, political scientist Simon Jackman said research shows that an efficiency gap above 7 percent in the first election after redistricting indicates that a state house map will continue to favor the winning party in subsequent elections.
In a recent case challenging North Carolina's congressional districts, Jackman suggested that an initial election efficiency gap of at least 7.5 percent in a state with more than 15 U.S. House districts should attract scrutiny. For states with 7 to 15 congressional districts, he put that efficiency gap threshold at 12 percent.
He did not analyze states with fewer districts, because each change in party control of a particular seat can have a larger impact on the efficiency gap.
The AP used similar efficiency gap thresholds when analyzing the 2016 data.
Legislators and governors are responsible for redistricting in many states. Some experts have suggested that partisan gerrymandering would be reduced if independent commissions were in charge of the task.
Shortly before the last round of redistricting, California voters adopted an independent citizens' commission for both congressional and state legislative reapportionment. In the 2016 elections, Democrats won more than two-thirds of the state Assembly seats and almost three-fourths of California's U.S. House seats.
But California is a predominantly Democratic state, and the AP's efficiency gap analysis found that the large seat margins were close to what would be expected based on Democrats' share of the vote.