By comparing a specific redistricting plan to an ensemble of plans, we evaluate whether the plan translates individual votes to election outcomes in an unbiased fashion. Explicitly, we evaluate if a given redistricting plan exhibits extreme statistical properties compared to an ensemble of nonpartisan plans satisfying all legal criteria. Thus, we capture how unbiased redistricting plans interpret individual votes via a state's geopolitical landscape. We generate the ensemble of plans through a Markov chain Monte Carlo algorithm coupled with simulated annealing based on a reference distribution that does not include partisan criteria. Using the ensemble and historical voting data, we create a null hypothesis for various election results, free from partisanship, accounting for the state's geo-politics. We showcase our methods on two recent congressional districting plans of NC, along with a plan drawn by a bipartisan panel of retired judges. We find the enacted plans are extreme outliers whereas the bipartisan judges' plan does not give rise to extreme partisan outcomes. Equally important, we illuminate anomalous structures in the plans of interest by developing graphical representations which help identify and understand instances of cracking and packing associated with gerrymandering. These methods were successfully used in recent court cases. Supplementary materials for this article are available online.
We develop methods to evaluate whether a political districting accurately represents the will of the people. To explore and showcase our ideas, we concentrate on the congressional districts for the U.S. House of Representatives and use the state of North Carolina and its redistrictings since the 2010 census. Using a Monte Carlo algorithm, we randomly generate over 24,000 redistrictings that are non-partisan and adhere to criteria from proposed legislation. Applying historical voting data to these random redistrictings, we find that the number of democratic and republican representatives elected varies drastically depending on how districts are drawn. Some results are more common, and we gain a clear range of expected election outcomes. Using the statistics of our generated redistrictings, we critique the particular congressional districtings used in the 2012 and 2016 NC elections as well as a districting proposed by a bipartisan redistricting commission. We find that the 2012 and 2016 districtings are highly atypical and not representative of the will of the people. On the other hand, our results indicate that a plan produced by a bipartisan panel of retired judges is highly typical and representative. Since our analyses are based on an ensemble of reasonable redistrictings of North Carolina, they provide a baseline for a given election which incorporates the geometry of the state's population distribution.
Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that adheres to realistic and non-partisan criteria. Using the sampled redistricting plans and historical voting data, we produce an ensemble of elections that reveal geo-political structure within the state. We showcase our methods on the two most recent districtings of NC for the U.S. House of Representatives, as well as a plan drawn by a bipartisan redistricting panel. We find the two state enacted plans are highly atypical outliers whereas the bipartisan plan accurately represents the ensemble both in partisan outcome and in the fine scale structure of district-level results.Gerrymandering | Redistricting | Monte Carlo Sampling I n the 2012 NC congressional election, over half the total votes went to Democratic candidates, yet only four of the thirteen congressional representatives were Democrats. Furthermore, the most Democratic district had 29.63% margin of victory, whereas the most Republican district had a 13.11% margin of victory. These results may be due to political gerrymandering or, alternatively, be natural outcomes of NC's geo-political structure as determined by the spatial distribution of partisan votes.To probe the geo-political structure and its effect on election outcomes we (i) sample from the space of congressional redistricting plans that adheres to non-partisan redistricting criteria; (ii) we simulate an election with each of our sampled redistricting plans using the actual partisan votes cast by North Carolinians in the 2012 and 2016 congressional elections; and (iii) we aggregate election results to construct the distributions of partisan vote balance on each district and of the congressional delegation's partisan composition. Districts that do not respect typical election results are considered gerrymandered. When a districting is gerrymandered, the congressional delegation's partisan composition may be not representative of what is typical.Having probed the impact of the geo-political structure, we analyze three specific districting plans: the two most recent districting plans of NC for the U.S. House of Representatives and a plan proposed by a bipartisan panel of retired NC judges. By situating the election outcomes of these three districting plans in our sampled ensemble, we determine whether the three districting plans contain unlikely partisan favoritism and thwart the underlying geo-political structure, as expressed by the people's votes, by shifting each district's partisan vote balance significantly away from what is typical. MethodsTo sample from the space of congressional redistricting plans, we construct a family of probability distributions that are concentrated on plans adhering to non-partisan design criteria from proposed legislation. The non-partisan design criteria ensures that
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