The Signature of Gerrymandering

Our Quantifying Gerrymandering group at Duke generated an ensemble of over 24,000 redistricting plans, sampled from a probability distribution placed on the collection of redistricting plans.  The ensemble was used to evaluate the 2012 and 2016 congressional district plans enacted by the NC General Assembly.  The two enacted plans were both found to be statistical outliers in the context of the ensemble of 24,000 plans; this outlier analysis formed the central argument of Jonathan Mattingly’s testimony in Common Cause v. Rucho.

In the outlier analysis, the most obvious statistic to consider is the partisan makeup of the congressional delegation each map produces.  The following histograms show that the 2012 maps (NC2012) and 2016 maps (NC2016) produce unlikely results.  In contrast, a map produced by a bipartisan panel of retired judges (Judges) produces typical results.

However, this simple analysis does not tell a complete story: In particular, as shown in the discussion of Firewalls,  a map can produce quite typical results for some elections and outlier results for other elections.

When analyzing the ensembles of predicted election results, different elections probe different elements of a redistricting plan’s structure.  A redistricting plan yields atypical election results only when the plan’s overall structure is anomalous in a way that is relevant to a particular election.   In short, the same plan can yield both anomalous and typical results for different elections, however some plans always give typical, expected results. Continue reading “The Signature of Gerrymandering”

Marginal Box-Plots: Summarizing what is Typical

One of the principle visualizations we have used to explore and and communicate our results is the Marginal Box-plot. Marginal box plots were one of the principle graphics presented in Redistricting: Drawing the line Evaluating Partisan Gerrymandering in Wisconsin, and the  group’s testimony in Common Cause v. Rucho.

The box-plots give a way to visually spot anomalous properties in a given redistricting plan by summarizing the structure of a typical plan, drawn without overt partisan considerations. For example, they can help identify what districts have been packed or cracked, showing which districts have many more or many less votes for a certain party than expected. The marginal box-plot give a baseline with which a given map should be compared.

Two prototypical examples of marginal box-plots are giving below. They summarize what we would expect  from redistricting of  North Carolina in to 13 Congressional districts and viewed through the lens of the actual votes cast in the 2012 and 2016 congressional elections.

Box-plot summary of districts ordered from most Republican to most Democratic, for the congressional voting data from 2012 (left) and 2016 (right).

Continue reading “Marginal Box-Plots: Summarizing what is Typical”

Hearing the Will of the People

Democracy is typically equated with expressing the will of the people through government. In a Republic, the people elect representatives who then act on their behalf and derive their political mandate from having won the election.

Possible corruption of the  electoral results is often framed in terms of voter suppression, voter fraud, or the undo sway of money on people’s votes. Once the votes are collected, once the access to information and the ballot box is unfettered, all that remains to register the will of the people is to count each vote once and only once.

Yet,  by varying how districts are drawn one can cause tremendous variation  in the outcome of the elections without changing a single vote. There is so much variability, that one might wonder if the effect is greater all the previously mentioned effects combined.  Continue reading “Hearing the Will of the People”

Gerrymandering is Not about Oddly Shaped Districts

It is tempting to assume that gerrymadnering requires the presence of oddly shaped districts.  After all, the term gerrymandering derives from the salamander-shaped maps produced by Massachusetts’s 1812 Governor Elbridge Gerry, and pictures of that meandering district are practically required in any discussion of gerrymandering.

The story goes that the irregularly shaped boundary attempts to include or exclude particular voters from the district.  Although irregular boundaries might well cause one to suspect gerrymandering, it is quite possible for a gerrymandered map to have quite regular districts. Oddly shaped districts, such as like North Carolina’s 12th congressional district and Pennsylvania’s 7th congressional district, make provocative tee-shirts and posters, but they are  only a symptom and not the point of Gerrymandering . Continue reading “Gerrymandering is Not about Oddly Shaped Districts”

Drawing New Maps for Pennsylvania

The  recent court ruling in Pennsylvania invited  “all parties and interveners” to submit their own maps to replace the maps which have been ruled unconstitutional.  (See also here.)

In the interest of facilitating such maps and their analysis, the Duke Quantitative Gerrymandering group is making  available our processed and cleaned map files and associated data at the following public git repository.

A local copy can be downloaded with

git clone

We encourage those who produce maps to share them with us.

Quantifying Gerrymandering : Data+ 2016

The evolution of the project continued with this second Data+ group. Because of our interaction and collaboration with the  Beyond Gerrymandering project, we again concentrated on North Carolina.

A new code base in Java was written. The version was tested carefully for reliability and correctness to a level beyond what had been done before.

Because of its increased efficiency longer runs could now be used.

Quantifying Gerrymandering : Data+ 2015

The webpage found here summarizes the work of the Data+ team during the summer of 2015. The work built on the previous summers work described in Redistricting and the Will of the People.

For the first time in the work the county splitting and not conforming to the VRA were penalized in the score function used to construct the measure. A number of different states were considered in this work.

For this iteration of the project, a new code base was written in Julia. Unfortunately some unidentifiable memory leaks (maybe in the language itself) limited the length of the runs posible.

Some middle bugs in this version of the code were corrected in the next version of the project initiated in the Data+ 2016 project. That work is the basis for Redistricting : Drawing line .