Carnegie Mellon University
January 05, 2022

Debunking Popular Conceptions About Gerrymandering

New Research Offers a Better Way to Overcome the Challenges of Electoral Districting

Recent increases in polarization in the United States have led to concern about the competitiveness of electoral districts as well as gerrymandering. Models for political districting have been devised for more than 50 years, but they are almost exclusively concerned with the geographical layout of districts.

In a new working paper, researchers analyzed political districting without geographical constraints to determine how to design an appropriate optimization model. Their analysis reveals serious issues with current ways to calculate how districts are drawn and from these, they propose ways to overcome existing challenges.

The analysis, by researchers at Carnegie Mellon University (CMU), Boston University (BU), and the University of Sydney, is published as a working paper.

“The term gerrymandering refers to the salamander-like shape of districts that are contrived to benefit a certain party, but a fundamental problem with gerrymandering is not the shape of the districts, but the unfair representation that results,” explains John N. Hooker, Professor of Business Ethics and Social Responsibility at CMU’s Tepper School of Business, who co-authored the study.

Researchers used elementary algebra to analyze fair districting without considering geography. Their model assumes that there are two political parties (though it can be expanded to include multiple parties or interest groups). In their analysis, they looked at what fraction of the voting population was aligned with the two parties, and which was the majority party. They examined how to design districts so a given number are in the majority.

Based on their model, they identified theoretical limits of gerrymandering. For example, clever districting can ensure that a party that receives only 25% of the votes can control the legislature. In addition, competitiveness (the chance that the minority party can win future elections), is sharply at odds with proportionality or proportional representation, the idea that the fraction of districts that favor a given party is roughly the fraction of people who belong to that party. Hooker points out that “when individual districts are dominated by a single political party, their representatives may be less inclined to compromise, which can result in a more partisan legislature.”

The model also reveals a fundamental flaw in the much-discussed efficiency gap criterion for fair districting. The efficiency gap measures the extent to which political parties differ in how many of their votes are “wasted.” Minimizing the efficiency gap is consistent with highly nonproportional representation and extreme non-competitiveness, so it is unsuitable as an objective.

To address these problems, researchers sought ways to retain proportionality while achieving competitiveness in most districts, with possibly wider margins of perhaps 20% in the remaining districts. They found that a satisfactory degree of proportionality was consistent with a surprisingly large number of highly competitive districts, which they suggest is a practical objective for the districting problem.

The authors suggest that an optimization model for redistricting should focus on two primary goals: fair representation without gerrymandering and avoidance of excessive polarization. Neither of these goals is fundamentally geographical in nature, and the conflict between them can be kept to a minimum by avoiding geographical constraints when possible.

“We are not opposed to the use of geographical constraints because they can serve a legitimate purpose,” says coauthor Gerdus Benadè, Assistant Professor of Information Systems at BU. “But the districting problem can be better understood, and more satisfactory optimization models can be developed, by viewing geography as a side constraint rather than a central element of the model.”


Summarized from a working paper, Political Districting Without Geography, by Benadè G (Boston University), Ho-Nguyen, N (University of Sydney), and Hooker, JN (Carnegie Mellon University). Copyright 2021. All rights reserved.