Redistricting, Courts, Challenges and Potential Solutions

6 min readNov 30, 2021

Gerrymandering can show up in many forms. It would be beneficial to cover some of the types. Racial gerrymandering involves a minority group subject to voting strength dilution; partisan gerrymandering is where one party controls the redistricting process and aims to exaggerate its political dominance by forcing an increase in election wins. Incumbent gerrymandering involves officials creating districts that ensure incumbents from both sides stay in power which we witnessed in California during the 2000s.

When it comes to gerrymandering, two types of districts are of concern. They are congressional and legislative districts. The mechanism by which redistricting takes place opens the door for incumbent politicians to take advantage of the redistricting process and shift election outcomes in their favor. In recent years multiple high-profile court hearings have shed light on the lack of a mechanism to understand the intention behind district maps proposed. In Gill v. Whitford (Gill v. Whitford, 2018), Wisconsin democrats challenged district maps drawn by the Republican majority in the state assembly. The Court ruled plaintiffs failed to demonstrate personal harm as a result of partisan gerrymandering. The plaintiff’s argument was based on the efficiency gap [1]. An idea introduced by Stephanopoulos and McGhee considers the sum of wasted votes across districts in a state. Wasted votes consider two values. For the winning party, anything over half of the margin needed to win is considered wasted. For the losing party, all of its votes within a district are considered wasted. The difference between the wasted votes for winner and loser is summed. This tidy statistic quantifies how many votes across the state are disproportionately being packed or cracked into districts. However, it fails to paint a complete picture of the state map, as indicated by the court ruling.

In Rucho v. Common Cause (Rucho v. Common Cause, 2019), North Carolina Republicans took to the Supreme Court to overturn a 2016 ruling by the North Carolina district court (Common Cause v. Rucho, 2018). The district court ruled that North Carolina’s 2016 Congressional Redistricting plan constitutes partisan gerrymandering in violation of Article I of the Constitution, the First Amendment. The main point of argument revolved around packing and cracking voters. This process involves either clumping like-minded voters into a few districts or splitting small groups into multiple districts. However, this ruling was overturned by the Supreme Court. The Supreme Court concluded partisan gerrymandering claims are not justiciable. They present political questions beyond the reach of federal courts.

I hope the court rulings I discussed have convinced you of the challenges of understanding the redistricting process. Imagine the neighborhood you live in. What are the key features that bring your neighbors together? What matters to you and your neighbors the most? Are there overlaps or conflicts in what you find essential? Now, what if I asked you to draw boundaries around your communities of interest. Could you accomplish this task? The legal definition of communities of interest would be in the realms of political, social, or economic interests. The questions I asked meant to get you to think as if you were in the position of redistricting a state. The proposed maps will have a tremendous impact on our nation’s fabric and influence policymaking in many aspects of our society. Understanding the more profound implications of the proposed maps is a critical step for any positive development.

There have been positive developments in the redistricting process. The introduction of independent redistricting commissions allows us to remove the incumbent politicians from the redistricting process. However, only eight states have adopted commissions for congressional maps and fourteen for drawing legislative maps. This process, however, is still not perfect since outside factors such as lobbying groups can still affect decisions of commissions. Lack of understanding of district maps being proposed, coupled with the political division brewing in the United States, is a dangerous problem. Research shows we are voting closer to party lines more than ever. However, comparing values of the extreme right and extreme left of the political spectrum, we find a lot in common between them. We human beings are complex with diverse needs, but there are overlaps in what we care about when we vote.

Most states demand that districts be compact. There is no precise definition in law for what it means to be compact. Some states use political boundaries such as cities, counties, etc., as measures for compactness. Dispersion, “the degree to which the district spreads from a central core” [1], is another measure used. We can use Polsby Popper Compactness [2], which compares a district’s area to perimeter ratio to the corresponding ratio for a circle. The output of the formula lies between 0–1, with 1 indicating maximal compactness. What makes pp compactness effective is that it’s very sensitive to both physical geography and map resolution. Arizona’s redistricting commission chose the method in 2000.

PP compactness and Efficiency gap can help us quantify the intention of maps; however, they cannot paint a complete picture. We need to combine these measurements with updated data on the needs and wants of people. In order to achieve this, we can combine census data with conversation pieces with residents at each precinct using an approach similar to ourStory[3]. This can allow us to create a framework for collecting and analyzing authentic voices containing the system’s demands and shortcomings. Putting these together can quantify how the communities of interest are connected and disconnected in maps.

To study the implication of compactness and the efficiency gap, we need to represent districting as a mathematical object. This involves defining a districting system that takes as input population size and number of desired districts. The state is described as a grid, where nodes represent voters and edges represent the physical connection. The attributes of voters can be expanded to represent multiple interests.

We have developed a tool that allows us to study quantifications used in Courts. The tool uses a minimum-cost flow optimization approach to implement a districting algorithm based on ideas introduced in “Balanced power diagrams for redistricting” by Cohen-Addad, Klien, and Young. The tool allows us to create sample spaces of districts represented as a grid with voter preferences assigned to voters in a randomized fashion with various levels of zooming for resolution of diversity. The different levels of resolutions for the distribution of voters concerning party preference combined with the districting algorithm can help us paint a picture of how efficiency gap and compactness are affected. Our current focus is on understanding the impact of homogeneity on the ratio of state-wide votes over wins.

Using the tool we can simulate sample spaces for party preference spread with various levels of resolution. Similar to the figure below.

We can then translate this population spread to district assignments and calculate the quantification I’ve discussed earlier. Please access the PG-Calculator here.

Let us consider a sample of 2850 instances where the number of voters ranges from 100–28000. The figure below shows the distribution of total votes and K (number of districts.) N here represents the resolution at which we create homogeneity of the population with respect to party preference.

K distribution based on N

We can further explore the relationship between the efficiency gap and Polsby-Popper Compactness based on various N values.

Efficiency Gap vs PP-Compactness based on N

The result above is based on a small sample of possible outcomes. This problem suffers from a combinatorial explosion. Due to this studying, all possible outcomes become extremely difficult. I am currently producing larger sample spaces using high-performance computer clusters. If you are interested in collaborating on this project please reach out to me via

Demo of Partisan gerrymandering calculator


[1] Justin Levitt. All about redistricting: Professor Justin levitt’s guide to drawing the electoral lines. accessed November 2021.

[2] Daniel D. Polsby and Robert D. Popper. The third criterion: Compactness as a procedural safeguard against partisan gerrymandering. 9 Yale L. Pol’y Rev., 1991.

[3] Bridgit Mendler. (2020). Our Story: Dispute system design technology for stakeholder inclusion. Masters’ Thesis, MIT Media Lab.