[Paper Review] Redistricting and the Will of the People

JC Mattingly, Christy Vaughn|arXiv (Cornell University)|Oct 29, 2014

Electoral Systems and Political Participation1 references19 citations

TL;DR

This paper proposes a non-partisan probability distribution for congressional redistricting in North Carolina based on population equality and district compactness, using Markov Chain Monte Carlo (MCMC) sampling to generate random districtings. When the 2012 election results were re-tabulated under these random districtings, the average number of Democratic representatives was 7.6, with 95% of outcomes between 6 and 9—dismally contrasting the actual 4 Democrats elected, revealing that redistricting, not voter preference, largely determined the outcome.

ABSTRACT

We introduce a non-partisan probability distribution on congressional redistricting of North Carolina which emphasizes the equal partition of the population and the compactness of districts. When random districts are drawn and the results of the 2012 election were re-tabulated under the drawn districtings, we find that an average of 7.6 democratic representatives are elected. 95% of the randomly sampled redistrictings produced between 6 and 9 Democrats. Both of these facts are in stark contrast with the 4 Democrats elected in the 2012 elections with the same vote counts. This brings into serious question the idea that such elections represent the "will of the people." It underlines the ability of redistricting to undermine the democratic process, while on the face allowing democracy to proceed.

Motivation & Objective

• To develop a non-partisan probability distribution over congressional redistrictings that emphasizes population equality and compactness.
• To assess how sensitive election outcomes are to the choice of district boundaries, independent of voter preferences or partisanship.
• To determine whether the actual 2012 election outcome in North Carolina reflects the typical outcome under random, fair redistrictings.
• To provide a statistical benchmark for evaluating whether a redistricting plan subverts the will of the people as expressed in vote totals.
• To demonstrate that redistricting can dramatically alter election outcomes even with identical vote shares, undermining democratic representation.

Proposed method

• Construct a graph where vertices represent voting precincts (VTDs), with split VTDs used to handle multi-district precincts.
• Define a probability distribution over redistrictings using only population balance and compactness, avoiding any partisan, racial, or socioeconomic data.
• Use the Metropolis-Hastings MCMC algorithm to generate effectively independent samples from this probability distribution.
• Approximate split VTD populations and areas as half of the original VTDs to maintain population balance in the model.
• Retabulate the 2012 U.S. House election results under each sampled redistricting using actual vote counts to determine the number of Democratic representatives.
• Analyze the distribution of Democratic seats across all sampled redistrictings to assess typicality and fairness.

Experimental results

Research questions

• RQ1 How does the number of Democratic representatives vary across a large ensemble of randomly generated, non-partisan redistrictings for North Carolina?
• RQ2 To what extent does the actual 2012 election outcome (4 Democrats) deviate from the typical outcome under fair redistricting?
• RQ3 Can a probability model based solely on compactness and population equality serve as a benchmark for evaluating the fairness of a redistricting plan?
• RQ4 Is the observed discrepancy between vote share and representation in North Carolina’s 2012 election due to gerrymandering or inherent geographic constraints?
• RQ5 What is the range of possible outcomes for the same vote totals under reasonable, non-partisan redistricting schemes?

Key findings

• The average number of Democratic representatives elected under randomly sampled, non-partisan redistrictings was 7.6, indicating a significant deviation from the actual 4 Democrats elected.
• Ninety-five percent of the randomly sampled redistrictings produced between 6 and 9 Democratic representatives, showing that 4 is an outlier in the fair distribution.
• The actual 2012 outcome is statistically unlikely under a fair redistricting model, suggesting that the result does not reflect the will of the people as expressed in vote totals.
• The current districting plan increases the most populous district’s population share from 14% to an average of 11% in the model, indicating improved population balance.
• The results demonstrate that redistricting has a profound impact on election outcomes, even when vote shares remain constant, undermining the legitimacy of the mandate.
• The study provides a statistical framework to identify redistrictings that are atypical and potentially subversive of democratic representation, even without using partisan or racial data.