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”