A Computational Approach to Measuring Vote Elasticity and Competitiveness

ABSTRACT

The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states’ reform efforts has been the inclusion of competitiveness metrics, or scores that evaluate a districting plan based on the extent to which district-level outcomes are in play or are likely to be closely contested.

In this article, we examine several classes of competitiveness metrics motivated by recent reform proposals and then evaluate their potential outcomes across large ensembles of districting plans at the Congressional and state Senate levels. This is part of a growing literature using MCMC techniques from applied statistics to situate plans and criteria in the context of valid redistricting alternatives. Our empirical analysis focuses on five states—Utah, Georgia, Wisconsin, Virginia, and Massachusetts—chosen to represent a range of partisan attributes. We highlight situation-specific difficulties in creating good competitiveness metrics and show that optimizing competitiveness can produce unintended consequences on other partisan metrics. These results demonstrate the importance of (1) avoiding writing detailed metric constraints into long-lasting constitutional reform and (2) carrying out careful mathematical modeling on real geo-electoral data in each redistricting cycle.

KEYWORDS:

• Competitiveness
• Gerrymandering
• Markov chains
• Redistricting

Notes

1 Notes

Some reform measures explicitly provide for a firewall between partisan-blind and partisan-aware parts of the process. For instance, Utah’s successful ballot initiative in 2018 requires the maps to be drawn without considering partisan data but requires the expected partisan behavior to be measured before a plan can be approved (Utah Code n.d.). Arizona requires similar behavior from its redistricting commission; the relevant portion of the redistricting law says that “Party registration and voting history data shall be excluded from the initial phase of the mapping process but may be used to test maps for compliance…” (Arizona State Constitution n.d.). In these cases, the process is designed to prevent mapmakers from directly optimizing for the metrics and instead sets up a failsafe against intended or unintended partisan skew.

2 For instance, consider this language in Colorado’s recent redistricting reform legislation: “Competitive elections for members of the United States House of Representatives provide voters with a meaningful choice among candidates, promote a healthy democracy, help ensure that constituents receive fair and effective representation, and contribute to the political well-being of key communities of interest and political subdivisions” (Colorado State Constitution n.d.).

3 The only reason not to consider state House plans is that House districts tend to be too small to be made out of whole precincts while maintaining tolerable population deviation. Precincts are the smallest level at which we have authoritatively accurate election outcomes, which are a crucial element of this style of analysis. Vote results can be prorated to smaller units, but this is done at the cost of a potentially significant loss of accuracy.

4 With the recombination technique used here, collecting 100,000 plans from a Markov chain is shown to be enough in many circumstances to obtain a consistent distribution of sample statistics, regardless of starting point. See DeFord, Duchin, and Solomon (2019) and its references for details.

5 This rule compares interestingly to the measure of competitiveness used by the 538 Atlas of Redistricting (Bycoffe et al. 2018). The Atlas project defined districts in the range from D + 5 to R + 5 as competitive, using the CPVI metric described in Section 2.3. Under their vote modeling, this corresponds to projected probabilities of approximately 18%–82% of electing a candidate from a given party.

6 That is, having $\text{EG}\approx 0$ requires having a tight relationship between overall vote share and overall seat share, with each additional percentage point of votes calling for two additional percentage points of seats. Since seats must turn out in a particular way to satisfy the EG test, there is a completely different reason that it is at odds with competitiveness: competitive seats introduce uncertainty and the potential for an unpredictable EG score (Bernstein and Duchin 2017).

7 Indeed, publications by Stephanopoulos–McGhee sometimes use this full definition of EG and sometimes use the “simplified formula” without the N term. Converting from Veomett’s notation to ours and letting $s=S/k$ and ρ be the ratio of average turnout in districts won by Party A to those won by Party B, we have $N=\frac{s(s-1)(1-\rho )}{s(1-\rho )+\rho }$. This vanishes in the equal-turnout case ρ = 1.

8 Clean Missouri prescribes that the vote pattern be constructed from the last three races for Governor, Senate, and President. At the time of writing, this amounts to a $D_0=50.3$, but when it is computed in 2021 it is likely to drop to the mid-40s. Interestingly, the number of competitive districts required by the rule is barely sensitive to the value of D₀.

9 For values of D₀ more extreme than 30–70, the allotment for close seats actually goes down as the efficiency gap demands virtually all safe seats for the majority party.

10 The underlying geographic and partisan data for each state was originally obtained from the following sources. Georgia: Geography from the Georgia General Assembly Legislative and Congressional Reapportionment Office (Georgia Legislative and Congressional Reapportionment Office 2019); partisan data from MIT Elections Data and Science Lab (MEDSL) (MIT Election Science Data Labs 2019). Utah: Geography from the Utah Automated Geographic Reference Center (Utah Automated Geographic Reference Center 2019); partisan data from MEDSL. Wisconsin: All geographic and partisan data from the Wisconsin Legislative Technology Services Bureau (Wisconsin Legislative Technology Services Bureau 2019). Virginia: All geographic and partisan data from the Princeton Gerrymandering Project OpenPrecincts project (Princeton Gerrymandering Project 2019). Massachusetts: Geography from the Massachusetts Secretary of the Commonwealth and partisan data from the Massachusetts Secretary of the Commonwealth Elections Division (Massachusetts Secretary of the Commonwealth Elections Division 2019). Staff of the Metric Geometry and Gerrymandering Group joined population data from the 2010 US Census to these datasets by aggregating up from census blocks, then used geospatial tools to clean the geographical data. The processed shapefiles and metadata are publicly available for download (MGGG 2019).

11 As described in DeFord, Duchin, and Solomon (2019), ReCom produces plans with compactness scores in range of human-made plans without any need to impose additional compactness constraints. Compactness is measured by a discrete metric called cut edges, which counts how many pairs of units were adjacent in the state but are assigned to different districts—these are the edges that would have to be cut to separate the whole graph into its district subgraphs.

12 Most states balance Congressional districts to within one person, but 2% balanced plans can readily be tuned to tight balance by a skilled human mapmaker. With 1% or 2% deviation, we get efficiently moving Markov chains. In other studies, we have confirmed that loosening or tightening population balance does not have substantial impacts on partisan summary statistics (DeFord and Duchin 2019).

13 The standard narrative around mean-median scores holds that MM = 0.05 means that the Republican party could expect half of the seats with only 45% of the votes.

14 In a similar vein, there is growing evidence that the MM score is not performing as advertised to signal meaningful partisan advantage (DeFord et al. 2019). Nonetheless, we use it here to highlight that competitiveness may not be independent of other popular partisan indicators.

15 For example, the CVPI values use a slightly Democratic-favoring baseline as a result of the popular vote in the 2016 presidential election, which makes it slightly easier to make competitive districts in Democratic-leaning states and slightly harder in Republican-leaning ones. Additionally, the 538 maps had constraints on the number of majority-minority districts.

Additional information

Funding

The authors gratefully acknowledge the generous support of the Prof. Amar G. Bose Research Grant and the Jonathan M. Tisch College of Civic Life.