The article talks about a challenge to the Wisconsin state redistricting process that successfully used this concept of "efficiency gap." The case has been appealed to the US Supreme Court, so it's something to pay close attention to.
While double checking, I came across a New Republic article written by Nicholas Stephanopoulus who was quoted in the Slate article. It seemed more appropriate to go to the horse's mouth for my quotes about 'efficiency gap.'
Stephanoupoulus begins by pointing out that while the Supreme Court isn't for gerrymandering, litigants haven't come up with solutions that they are comfortable with. He says they have hinted at some ideas such as Justice Stevens' idea of 'partisan symmetry.' So Stephanopoulos and Eric McGhee have come up with what he claims would test for that, though he calls it something a little different.
"No litigants have seized this opportunity yet, but they should. To assist them, McGhee and I have devised a new metric of partisan symmetry called the efficiency gap. The efficiency gap is simply the difference between the parties’ respective wasted votes in an election, divided by the total number of votes cast. Wasted votes are ballots that don’t contribute to victory for candidates, and they come in two forms: lost votes cast for candidates who are defeated, and surplus votes cast for winning candidates but in excess of what they needed to prevail. When a party gerrymanders a state, it tries to maximize the wasted votes for the opposing party while minimizing its own, thus producing a large efficiency gap. In a state with perfect partisan symmetry, both parties would have the same number of wasted votes.
Suppose, for example, that a state has five districts with 100 voters each, and two parties, Party A and Party B. Suppose also that Party A wins four of the seats 53 to 47, and Party B wins one of them 85 to 15. Then in each of the four seats that Party A wins, it has 2 surplus votes (53 minus the 51 needed to win), and Party B has 47 lost votes. And in the lone district that Party A loses, it has 15 lost votes, and Party B has 34 surplus votes (85 minus the 51 needed to win). In sum, Party A wastes 23 votes and Party B wastes 222 votes. Subtracting one figure from the other and dividing by the 500 votes cast produces an efficiency gap of 40 percent in Party A’s favor.
The efficiency gap has several properties that make it ideal for measuring the extent of gerrymandering. First, it directly captures the packing and cracking that are at the heart of every biased plan. Surplus votes for winning candidates are the definition of packing, and lost votes for defeated candidates the essence of cracking. All a gerrymander is, in fact, is a plan that results in one party wasting many more votes than its opponent. The efficiency gap tells us exactly how big the difference between the parties’ wasted votes is."If you didn't read that carefully, here are some key terms:
Two Kinds of Wasted Votes - votes that didn't contribute to victory
Surplus Votes - those votes more than needed to win
Lost Votes - votes cast for candidate who was defeated
Efficiency Gap is simply the difference between the parties’ respective wasted votes in an election, divided by the total number of votes cast.
An extreme example was Pennsylvania where gerrymandering gave the Democrats lots of lost votes. From Republic Report:
"In Pennsylvania, one state in which the GOP drew the congressional districts in a brazenly partisan way, Democratic candidates collected 44 percent of the vote, yet Democratic candidates won only 5 House seats out of 18. In other words, Democrats secured only 27 percent of Pennsylvania’s congressional seats despite winning nearly half of the votes."
Democrats, who have been hurt badly by Republican control of redistricting after the 2010 census, are hoping this case could break open some opportunities for them. Here's a FairVote article from December 2016 looking at this case and the larger picture.