Gerrymandering and the Efficiency Gap

Learning Objectives

  • Understand the definition, history, and political consequences of gerrymandering

  • Be able to draw districts to that outcomes favor one party or another

  • Be able to calculate the efficiency gap for a state

  • Become familiar with real-world examples and current legislation/court cases relating to gerrymandering and the efficiency gap

  • Apply knowledge about gerrymandering and the efficiency gap to current politics

Common Core Standards and Mathematical Practices

7th Grade: Ratios and Proportional Relationships

7.RP.A.2 Recognize and represent proportional relationships between quantities.


7th Grade: Number Systems


7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Mathematical Practices

MP1. Make sense of problems and persevere in solving them.

MP2. Reason abstractly and quantitatively

MP3. Construct viable arguments and critique the reasoning of others.

MP4. Model with mathematics.

Key Terms

  • Apportionment: The process of assigning seats in a legislative body among different levels of government.

  • Census: A count, mandated by Article II of the U.S Constitution, of every resident residing within the United States that takes place once every decade.

  • Communities of Interest: Geographical regions where residents share a common interest or are of a similar demographic.

  • Cracking: Spreading opposition voters sparsely over a number of districts to minimize their voting power.

  • District: A political unit with boundaries that define which constituents/residents an elected official represents.

  • Hijacking: Redrawing district lines to force two incumbent politicians to run against each other, eliminating one of them in the process.

  • Incumbent: An elected official who is currently holding the seat up for election and is running for re-election.

  • Independent Redistricting Commission: a body, other than the usual state legislative bodies, established to draw electoral district boundaries in a fair and unpartisan way.

  • Kidnapping: Redrawing district lines so that an incumbent’s home address is now in a different district, where re-election may be more challenging.

  • Packing: Forcing opposition voters into a few conceded districts to minimize the number of representatives of the opposing party that are elected.

  • Stacking: Low-income, less-educated non-white voters are pushed into the same district as high-income, well-educated white voters. While the non-white voters appear to have a majority in the district, the white voters have a greater voter turnout.

Gerrymandering

The practice of dividing a territory into election districts in a way that gives one political party an unfair advantage in elections

What are voting districts?

  • Each state is split up into voting districts, which are redrawn every ten years according to the census

  • The winner of an election is determined by the number of districts a candidate wins

  • Districts are geographical areas whose borders are drawn by the party in power

  • Districts should not always be perfectly shaped. Sometimes districts are redrawn to give groups of people with shared beliefs more representation by allowing them to vote as a group and elect legislators who represent their interests

So, what is gerrymandering?

  • When voting districts are redrawn, the district lines are determined by the party in power at the time

  • While the original intention of district reshaping is to give a voice to everyone, these borders can be manipulated to serve a particular group of people. This is called gerrymandering

History of Gerrymandering

The term gerrymandering is named after the American politician Elbridge Gerry. In 1812, he signed a bill that created a salamander-shaped voting district in the Boston area along party lines, giving the republican party an advantage. The word salamander was combined with Gerry's last name to make gerrymander.

After the voting rights act of 1965, racial gerrymandering became prohibited. However, political gerrymandering is still legal as long as it is not too extreme.

There are a few general guidelines for the construction of districts as to avoid gerrymandering:

1) they must all be about the same population size

2) the districts should be compact; they should have a 'reasonable' shape

3) they should be contiguous (connected) - i.e. you can't have one district made up of two separate parts

4) they should not split counties or cities (as well as possible)

5) they should not split communities of interest

6) they should respect the voting rights act by providing representation for minority groups

Gerrymandering Practice

Let's take a closer look at how districts can be drawn to give a particular party an advantage.

Click here to try drawing your own districts!

You can also play a fun gerrymandering game here!

Packing Cracking

Packing and Cracking

The main two ways gerrymandering is accomplished are through packing and cracking.

Packing - a packed district is drawn to include as many candidates as possible for one party

Cracking - a cracked district has split up groups of the oppositions candidates in order to minimize their chances of winning (essentially diluting their power)

Stacking, hijacking, and kidnapping also occur:

Stacking groups low-income, less educated minorities together to create a perceived voting majority, but puts them in the same district as high-income, better-educated white voters who turn out to vote in greater numbers.

Hijacking redraws two districts in a way that forces two incumbents to run against each other in one district, ensuring that one of them will be eliminated.

Kidnapping moves an incumbent’s home address into another district where it will be more difficult for them to be reelected.

The Efficiency Gap

What is the Efficiency Gap?

The efficiency gap is a method devised by Nicholas Stephanopoulos and Eric McGhee in 2014 to test for gerrymandering. The efficiency gap tests if either party had a significant, systematic advantage in gaining election seats. In particular, the efficiency gap is good at detecting packing and cracking.

The efficiency gap is calculated by finding the difference between two parties' wasted votes and dividing that difference by the total number of votes.

Wasted votes are any votes cast for the losing candidate and all votes cast for the winning candidate beyond the minimum needed to win the election. (Eg. In a district with two parties running for a seat, with at least 6 votes needed to win, the winning candidate gets 10 votes and the losing candidate gets 7. All 7 of the losing candidate’s votes are wasted, while 2 of the winning candidate’s votes are wasted. The reason why only 2 are wasted and not 3 is because if the winning candidate had received only 7 votes they would have tied with the losing candidate.)

The efficiency gap is calculated using the following formula:

|(one party’s wasted votes) - (other party’s wasted votes)|

___________________________________________________

total number of votes


An efficiency gap greater than 7% is indicative of gerrymandering.


Note: the order in which you subtract one party’s wasted votes from another does not matter, since you are using the absolute value of the difference.

While the Red Party won 20/40 votes, which is 50% of the total vote, it only won one out of four seats. This is only 25% of total seats!

Let's try an example!

  1. Count the number of votes each party received in each district.

The Red Party won the first district with 10 votes.

The Blue Party won the second district with 7 votes to the Red Party's 3 votes.

The Blue Party won the third district with 7 votes to the Red Party's 3 votes.

The Blue Party won the fourth district with 6 votes to the Red Party's 4 votes.

2. Find the number of wasted votes for each party in each district.

In District one, the Red Party wasted 9 votes because it only needed 1 vote to win the district!

In District two, the Red Party wasted 3 votes because it lost, and the Blue Party wasted 3 votes because it would have won with 4.

In District three, the Red Party wasted 3 votes because it lost, and the Blue Party wasted 3 votes because it would have won with 4.

In District four, the Red Party wasted 4 votes because it lost, and the Blue Party wasted 1 vote because it would have won with 5.

3. Now let's find the efficiency gap!

First, let's add up the total number of votes cast:

10+7+3+7+3+6+4+9+1 = 40 votes

Add up all of the Red Party's wasted votes:

9+3+3+4 =19 votes

And the Blue Party's wasted votes:

0+3+3+1=7 votes

Let's calculate the efficiency gap!


|(one party’s wasted votes) - (other party’s wasted votes)| |19 - 7| 12

___________________________________________ ______ = ______ = .3 = 30%

total number of votes 40 40



According to the Efficiency Gap, there is evidence of gerrymandering here, because .3 > .07.

Flaws of the Efficiency Gap

The efficiency gap is useful as a quick tool for detecting partisan-based gerrymandering. The efficiency gap was presented as a solution to Justice Antony Kennedy's claim in a 2004 Supreme Court ruling on partisan gerrymandering, that if there were "a workable standard" to prove there is evidence of partisan gerrymandering, he may have ruled differently (The Atlantic). The efficiency gap is this solution, with several advantages:

  • Easy/simple to calculate

  • Based on real election results/data

  • Straightforward results

Yet despite the praise the efficiency gap has received, from mathematicians and politicians alike, it is not without its flaws.

  • The efficiency gap does not take into account political geography. Natural demographic differences/concentrations can be mistaken for manipulated packing. People with similar political mindsets tend to live in concentrated clusters; this is not a result of manipulated district boundaries (eg. Democrats being more concentrated in populous cities).

  • The efficiency gap may flag a party receiving x% of the seats, despite actually also receiving x% of the statewide vote, as partisan gerrymandering

  • The efficiency gap does not take into account non-partisan factors that might make one party receive a significantly larger share of votes than another (eg. an incumbent runs vs a newcomer)

In general, most critiques of the efficiency gap are the same as its advantage: it's far too simple. Gerrymandering is a highly nuanced issue, and reducing the detection of gerrymandering to a simple calculation does not take into account all of the complications of districting and partisan gerrymandering. This does not mean that the Efficiency Gap should not be used--rather, we need to be cautious and critical when using it, making sure to take its results with a grain of salt.

For more reading on the dangers of the Efficiency Gap:


Gerrymandering and the Efficiency Gap in the News!

Although racial gerrymandering has been outlawed, political gerrymandering is legal, so there are always gerrymandering cases in state and federal courts. However, sometimes states can racially gerrymander and act like it is political. It becomes the duty of the courts to determine what is political and what is racial gerrymandering. Here are some important and recent cases (note: these are not all of the gerrymandering cases in the courts; there are tons of contemporary examples).

U.S. Supreme Court (2019)

In 2019, North Carolina and Virginia filed suits challenging the constitutionality of their states' congressional districting maps as unconstitutional partisan gerrymandering. The Supreme Court ultimately decided that partisan gerrymandering can no longer be challenged in federal courts, and is instead a matter that must be left to the state courts. It's very difficult for a state to deal with gerrymandering, especially because the political party that has power often is doing the gerrymandering.

North Carolina (2019)

North Carolina's Superior Court issued an injunction in October of 2019 declaring that the current districts could not be used in the 2020 elections due to "extreme partisan gerrymandering." Although this type of gerrymandering is still legal, judges found that the district map would give Republican lawmakers a substantial advantage in 10 of North Carolina's 13 districts. Lawmakers had to redraw the districts or risk being unable to participate in the primary elections; the former and new district maps are shown ---------->

Gil v. Whitford (2016)

    • The Wisconsin State Supreme Court declared that the redistricting adopted by Wisconsin's Republican legislature in 2011 was an unconstitutional partisan gerrymander

    • In order to determine if gerrymandering had occurred, a three-judge federal panel used the efficiency gap (as well as two other secondary measures) to determine that Wisconsin districts had been gerrymandered with "bad intent and bad effect"

    • Wisconsin had an efficiency gap of 13% with the districts adopted in 2011!

Legislation Preventing Gerrymandering

Solutions to Gerrymandering

Gerrymandering allows the party in power to control the outcomes of elections and choose who has more say. When gerrymandering is allowed, elections are unfair. So what should we do?

One potential solution is to require states to use independent redistricting commissions to redraw their districts following the census.

    • Independent redistricting commissions are not made up of people from any one political party, so they are more fair.

    • As of 2020, 8 states use independent redistricting commissions for their congressional districts, and 14 use them for their state representatives.

    • If all states committed to having these commissions, it could eliminate partisanship in redistricting.

Can you think of any other solutions?