# Firewalls

A Firewall is a buffer used to block unauthorized access.  We adapt the term ‘Firewall,’ in the context of gerrymandering, to describe a districting plan that artificially protects the power of a political party.  What follows is an exposition on how we discovered a Firewall in the enacted districting plan for the Wisconsin General Assembly  that protects the Republican Party from losing the majority of the seats.

For districting plans of the Wisconsin General Assembly, we generate thousands of compliant redistricting plans.  To evaluate the enacted districting plan (the Act 43 plan), we ask if how many officials are elected by each party for each plan for a given a set of votes: Each plan in the ensemble will generate a certain number of Democrats and a complementary number of Republicans (ignoring independent candidates), and we can construct a histogram that measures the number of representatives from each party, out of the 99 available seats.

For example, when looking at the Wisconsin General Assembly districts, we construct histograms of the projected number of Republican elected officials that would have won based on 2012, 2014, and 2016 voting data.

The modes of these histograms are 55, 63 and 67 elected Republicans out of 99 available General Assembly seats for the 2012, 2014, and 2016 vote counts, respectively.  The increased number of seats over these years is consistent with the increased statewide fraction of the Republican vote, found to be 50.05%, 51.28%, and 52.9%  for the 2012, 2014, and 2016 vote counts, respectively.*  The histograms give a sense of what is typical for a three different sets of voting data.

In order to compare whether or not the enacted Act 43 Wisconsin redistricting plan is typical, we display the number of elected Republicans with the given voting data, and contextualize the Act 43 plan results within the histograms.

We find that there are 60, 63, and 67* elected Republicans for the Act 43 redistricting plan, under the 2012, 2014, and 2016 voting data, respectively.  This means that the 2014 and 2016 votes yield the most probable number of Republicans.   Only under the 2012 data, do we have an atypical result.

If we view each set of voting data as an individual test for typicality, we have passed two tests and failed one which, naively, may suggest that the Act 43 map may be reasonable.  But there is something strange about where the enacted map is typical and where it is not: When the number of expected Republican seats begins to approach half — meaning a loss of a Republican majority — we see an atypically large number of Republican representatives.

Three elections is hardly enough to draw any conclusions, so next, we redraw histograms for a variety of election data, and plot the histograms in the context of the statewide Republican vote fraction.  We also examine the predicted outcome of the Act 43 map under each set voting data and visualize the result of the enacted plan with a red circle.  We use voting data from the Wisconsin State (General) Assembly in the years 2012, 2014, and 2016 and denote these elections as WSA12, WSA14, and WSA16, respectively; Governor elections are denoted with GOV, United States House (congressional) races with USH, Presidential races with PRE, Secretary of State with SOS, and United States Senate with USS.

We find that for large statewide Republican vote fractions (above 51%), the number of projected Republican seats is always typical of the ensemble, typically obtaining the most probable result.  Once the statewide Republican vote fraction falls below 48% there is an abrupt change of behavior: The districting plans in the ensemble continue to react to the increased percentage of Democratic votes and the Democrats can expect to win a majority of the seats.  The enacted Act 43 plan, however is unaffected by the increased fraction of Democratic votes: From 51-54% statewide Democratic vote fraction (49-46% statewide Republican vote fraction) the Act 43 plan predicts there will be 54-56 Republican seats, meaning that they will comfortably maintain a majority.  In a very real sense, the Act 43 plan acts as a Firewall that prevents the Democrats from gaining majority.

As a second test for the Firewall, we return to analyzing only the voting data for the General Assembly, and adopt the uniform partisan swing hypothesis to test the effect of how the ensemble and Act 43 plans will behave under a variety of statewide partisan vote fractions.  We test the voting data over the 2012, 2014 and 2016 data, and analyze the projected number of elected Republicans when the statewide Republican vote fraction ranges from 45-55%.

The results are nearly identical to the first test, when using data form various elections.  In all cases, the Republicans maintain their majority for significantly lower statewide vote fractions than expected.  We can also see that under the 2012 and 2016 voting data, the voting structure predicts the Republicans will gain a super majority of the seats in a typical fashion — this means that the Republicans can expect to keep the majority, while giving their party a typical chance at winning a super majority.

We conclude that the enacted Act 43 plan may elect a typical number of Republican representatives for elections in which the statewide Republican vote fraction is large,  but that the enacted plan becomes atypical, strictly favoring the Republican Party,  when the Democrats threaten to regain the majority.  This is a Firewall within the Act 43, providing an artificial buffer to protect the Republican majority.