Using Spatial Methods to Combat Gerrymandering After the 2020 US Census

Mark Altaweel


The 2020 US Census will soon come to a conclusion and one result of this is that it will reallocate congressional representation for the next decade. State lawmakers will also be tasked with redrawing congressional districts.

Previously, the 2010 Census led to numerous allegations of gerrymandering. Research even suggests that 2010 could have been the most gerrymandered redistricting efforts in US history. Such results have now drawn more interests from geospatial experts to create better methods to measure gerrymandering.[1]

With the right spatial methods, however, it might be possible to avoid similar controversy after the 2020 Census concludes.

In October 2019, the state court in North Carolina struck down the state’s redistricting, finding severe gerrymandering efforts in the state. The decision was informed by numerous other maps that showed alternative scenarios of how representative districts could have been redrawn.

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Visualizing how a district can be gerrymandered to produce disproportionate outcomes.  Figure: M. Boli, CC BY 4.0, MediaWiki Commons
Visualizing how a district can be gerrymandered to produce disproportionate outcomes. Figure: M. Boli, CC BY 4.0, MediaWiki Commons

Mathematical Test and Gerrymandering

There have been mathematical tests applied to districts to determine if it has been gerrymandered. For instance, districts with disproportional representation of given demographics that are likely to vote for one party or evidence of demographics overly diluted across multiple district boundaries can be used to determine bias in district boundaries.

Other tests have also been developed that have looked at the spread of votes across districts to see if given districts have greater bias for one party.

In the 2019 case in North Carolina, the non-partisan group PlanScore used three tests, including the two mentioned, and a third test to show that in all three tests North Carolina demonstrated clear gerrymandering.

The third test in this case was called efficiency gap, where the votes that are ‘wasted’, or votes for the losing party, are tallied and the method measures if districts are too packed, that is too many voters for one party in one area, or cracked, or voters spread too thin for one party. If in such districts a high percentage of wasted votes would have had little effect on an outcome, then the result is a bias for the district in how it represents the population.

A screenshot from PlanScore's assessment of North Carolina's 2016 Redistricting Plan.  Captured September 30, 2020.
A screenshot from PlanScore’s assessment of North Carolina’s 2016 Redistricting Plan. Captured September 30, 2020.

Recently, computer simulations and tests that create alternative maps can also apply different tests to see if districts are too ‘packed’ or too ‘cracked’, that is dispersed, relative to other possible mapping. It is these ensemble approaches that researchers think can be used to measure for bias in the next round of redistricting likely to begin next year.[2]

Analyzing Spatial Shapes to Detect Gerrymandering

There are also other methods that have been developed, including those that depend on spatial shapes of districts to detect potential gerrymandering.

Shape compactness metrics help determine if given shapes of districts are oddly shaped. Metrics for roundness, convexity, and nearby similarity and context of other districts can be used to create a threshold that a given district is spatially very different from others and potentially gerrymandered.[3]

An analysis by The Washington Post found the 35th Congressional District to be among the top ten gerrymandered congressional districts. Maps created using Natural Earth data and the 16h Congressional District.
An analysis by The Washington Post found the 35th Congressional District to be among the top ten gerrymandered congressional districts. Maps created using Natural Earth data and the 16h Congressional District.

 Another method uses a combination of spatial boundaries and characteristics of the population and infrastructure in given areas to determine less biased districts. In this case, a capacitated double p-median problem with preference (CDPMP-P) approach is used. For spatial aspects, the method looks at boundaries and how they align relative to each other. Other factors assessed include population balance, preferences for potential facilities where polling can take place and installed, and possibilities for allocating multiple polling places.

In effect, the method uses spatial properties, how well the population is balanced in representation, and if the district is well provisioned to vote. Districts that score high in these categories are deemed to be less gerrymandered, while those that have biases and lack provisions for voting are more likely to be gerrymandered.[4]

What research has demonstrated is that gerrymandering is not only a problem in the United States but also for many representative democracies, particularly as population shifts often means fair representation requires some form of redistricting.

The challenge for geospatial communities is to not only create effective methods that can better determine what less biased district maps look like but these methods also need to be acceptable to the judiciary. In an earlier Supreme Court case, the justices ruled that expert created maps are not necessarily free of bias. The challenge, therefore, is to create approaches that appease different stakeholders and be as objective as possible in drawing district boundaries.  


[1]    For more on gerrymandering using the 2010 Census, see: Engstrom, R.L., 2020. Introduction to the Mini Symposium on Partisan Gerrymandering. Social Science Quarterly 101, 8–9.  

[2]    For more on redistricting methods and approaches applied to previous and forthcoming census results, see:

[3]    For more on measuring gerrymandering using spatial properties of districts, see:  Sun, S., 2020. Developing a Comprehensive and Coherent Shape Compactness Metric for Gerrymandering. Annals of the American Association of Geographers 1–21.

[4]    For more on the CDPMP-P approach, see:  Kim, K., 2020. A Spatial Optimization Approach for Simultaneously Districting Precincts and Locating Polling Places. ISPRS International Journal of Geo-Information 9, 301.


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About the author
Mark Altaweel
Mark Altaweel is a Reader in Near Eastern Archaeology at the Institute of Archaeology, University College London, having held previous appointments and joint appointments at the University of Chicago, University of Alaska, and Argonne National Laboratory. Mark has an undergraduate degree in Anthropology and Masters and PhD degrees from the University of Chicago’s Department of Near Eastern Languages and Civilizations.