The Supreme Court heard a case on Oct. 3 about whether Wisconsin Republicans gave themselves a guaranteed GOP majority when they redrew the state’s legislative districts in 2011.
A new way to test for partisan gerrymandering is a key part of the plaintiffs’ argument — the efficiency gap. Here’s how it works.
In this imaginary state, there are 20 green voters and 30 purple voters. Even though there are more purple voters, a district plan can be drawn that stacks the odds for green lawmakers to control the state.


The partisan plan makes three cracked districts, putting four purple voters with six green voters and making it difficult for purple candidates to win. Boundaries in a cracked district are drawn in a way that intentionally dilute the vote.

Three cracked districts

Three cracked districts
Nine purple voters are packed into the two remaining districts with one green voter, where purple candidates will easily win.

Two packed districts

Two packed districts
To measure the efficiency gap for this plan, researchers would first count how many votes are wasted by each party. Wasted votes are those cast that do not contribute to victory.
Green candidates can win with a six-vote majority in the cracked districts, so four purple votes in each district are wasted. One green vote is wasted in the packed districts. Three purple votes are also wasted, since the purple candidate has more than the six vote-majority they need to win.

Vote cast above the simple majority needed to win
Vote cast in a district this party didn’t win

Vote cast above the simple majority needed to win
Vote cast in a district this party didn’t win
The difference between the wasted votes on each side is divided by the total number of votes to get the efficiency gap:

Wasted green votes
Wasted purple votes
2
-
18
= -16%
100
efficiency gap benefiting the green party

Wasted green votes
Wasted purple votes
2
-
18
= -16%
100
efficiency gap benefiting
the green party
The efficiency gap measurement was created by Nicholas Stephanopoulos, a University of Chicago law professor who is representing the plaintiffs in the Wisconsin case, and Eric McGhee, political scientist at the nonpartisan Public Policy Institute of California.
The measure "gives you, in a single number, an indication of which side is benefiting from all of the cracking and packing and how large of an advantage they have," Stephanopoulos said.
Here’s how this played out in a real state — Wisconsin. The state’s general assembly, the lower house of the legislature, has elections every two years:

2012
-10% efficiency gap benefiting Republicans
Majority
47%
52%
1%
Votes
Seats
62%
38%
Republicans won 61 seats
Democrats won 38 seats
23 elections were uncontested
Milwaukee
Madison
2014
-13% efficiency gap benefiting Republicans
Majority
55%
41%
2%
Votes
Seats
64%
36%
Republicans won 63 seats
Democrats won 36 seats
46 elections were uncontested
Milwaukee
Madison
2016
-10% efficiency gap benefiting Republicans*
Majority
52%
45%
3%
Votes
Seats
65%
35%
Republicans won 64 seats
Democrats won 35 seats
42 elections were uncontested
Milwaukee
Madison
* Efficiency gap figure for 2016 is from an
Associated Press analysis. Gaps for 2012 and
2014 were calculated by Simon Jackman.

2012
-10% efficiency gap benefiting Republicans
Majority
47%
52%
1%
Votes
Seats
62%
38%
Republicans won 61 seats
Democrats won 38 seats
Milwaukee
23 elections were uncontested
Madison
2014
-13% efficiency gap benefiting Republicans
Majority
55%
41%
2%
Votes
Seats
64%
36%
Republicans won 63 seats
Democrats won 36 seats
Milwaukee
46 elections were uncontested
Madison
2016
-10% efficiency gap benefiting Republicans*
Majority
52%
45%
3%
Votes
Seats
65%
35%
Republicans won 64 seats
Democrats won 35 seats
Milwaukee
42 elections were uncontested
Madison
* Efficiency gap figure for 2016 is from an Associated Press analysis.
Gaps for 2012 and 2014 were calculated by Simon Jackman.

2012
2014
2016
-10% efficiency gap benefiting Republicans
-13% efficiency gap benefiting Republicans
-10% efficiency gap benefiting Republicans*
Majority
Majority
Majority
47%
52%
1%
55%
41%
2%
52%
45%
3%
Votes
Votes
Votes
Seats
Seats
Seats
62%
38%
64%
36%
65%
35%
Republicans won 61 seats
Republicans won 63 seats
Republicans won 64 seats
Democrats won 38 seats
Democrats won 36 seats
Democrats won 35 seats
23 elections were uncontested
46 elections were uncontested
42 elections were uncontested
Milwaukee
Milwaukee
Milwaukee
Madison
Madison
Madison
* Efficiency gap figure for 2016 is from an Associated Press analysis. Gaps for 2012 and 2014 were calculated by Simon Jackman.
The map used since 2012 allows Republicans to keep winning control. Research submitted by the plaintiffs found “there is a 100% probability that all subsequent elections held ... will also have efficiency gaps disadvantageous to Democrats.”
In its defense, the state says its map “complies with traditional redistricting principles,” such as compactness. It also said the political geography of Wisconsin means Democratic voters tend to cluster in cities.
Packing can create the same effect. "That means that their supporters do not translate into representation," McGhee said. "It's a form of vote dilution."
How Wisconsin compares to other states
The efficiency gap measure can be used to calculate a score for any district maps, but the Wisconsin plans stand out in a state-by-state comparison submitted by plaintiffs to the court.
"There aren't many plans that are equivalently egregious as the Wisconsin map," Stephanopoulos said.
Here’s the efficiency gaps for 2012 and 2014 in the 41 U.S. states where the lower chamber of the legislature is elected by single-member districts.

2014
-13%
2012
-10%
Wisconsin
Efficiency
gap
Confidence
interval
-20%
-7%
0
7%
20%
RI
VT
Confidence
interval
CO
AK
HI
Efficiency gap
Map favors
Republicans
ME
KY
OR
CA
Map favors
Democrats
MA
MT
UT
NV
AR
IL
WA
CT
WV
NM
DE
Researchers propose a threshold of 7% to measure when a gap is too extreme
TN
IA
SC
TX
OK
PA
MN
GA
MO
OH
WY
NY
IN
Some swing states have low scores
KS
WI
NC
VA
MI
FL
-20%
--7%
0
7%
20%

2014
-13%
2012
-10%
Wisconsin
Efficiency
gap
Confidence
interval
-20%
-10%
-7%
0
7%
10%
20%
RI
VT
Confidence
interval
CO
AK
HI
Efficiency gap
ME
KY
OR
CA
MA
Map favors
Republicans
Map favors
Democrats
MT
UT
NV
AR
IL
WA
CT
WV
NM
DE
Researchers propose a threshold of 7% to measure when a gap is too extreme
TN
IA
SC
TX
OK
PA
MN
GA
MO
OH
WY
NY
IN
Some swing states have low scores
KS
WI
NC
VA
MI
FL
-20%
--10%
0
10%
20%

Wisconsin
Efficiency gap
2012: -10%
Confidence
interval
2014: -13%
20%
20%
Map favors
Democrats
RI
Confidence interval
VT
Efficiency gap
Researchers propose a threshold of 7% to measure when a gap is too extreme
10%
10%
HI
MA
AK
MT
KY
CO
7%
7%
AR
WV
ME
IL
OR
CA
SC
NV
TN
UT
IA
WA
DE
CT
OK
NM
TX
WY
0
0
PA
Some swing states have low scores
GA
MO
OH
MN
VA
IN
NY
-7%
-7%
WI
KS
NC
FL
-10%
-10%
Map favors
Republicans
-20%
-20%
The researchers cautioned that high efficiency gap scores aren’t the only way to measure whether partisan gerrymandering occurred — it’s one part of the plaintiffs’ argument that also considers the mapmakers’ intent and the one-person, one-vote doctrine, which says districts should have equal numbers of residents.
The court has previously decided that it’s illegal to draw district plans that harm minority voters, but they have never declared a partisan plan unconstitutional.
If the Supreme Court rejects the Wisconsin maps and decides to adopt the efficiency gap measurement in its decision, more states could see lawsuits.
Stephanopoulos said only states whose maps were drawn under unified control, where both chambers of the legislature and the governorship were controlled by the same party, could be challenged using the efficiency gap test.
About this story
Gerrymandering explanation from the Campaign Legal Center. State-by-state efficiency gap analysis for 2012 and 2014 from Assessing the Current Wisconsin State Legislative Districting Plan by Simon Jackman. Wisconsin efficiency gap figure for 2016 from the Associated Press. Wisconsin election results from the Wisconsin Elections Commission.
Originally published Oct. 2, 2017.
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