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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