The Idea Incubator/Improving Constituent Assignments to Representatives

Today in the United States constituents are assigned to representatives based on geographically defined electoral districts. This system is often criticized because it is subject to gerrymandering—the practice of shaping districts to help retain political power.

What fairer alternatives approaches to assigning constituents to representatives can we imagine?

A “striped district” approach would simply divide a state along horizontal latitudinal boundaries to create the required number of electoral districts. This retains the geographic proximity and continuity of today’s districts, while preventing any manipulation of the district boundaries. Each district is likely to include a more diverse population that will require the representative to consider a broader range of issues when representing constituents.

An “age range” approach abandons geographic bounds in favor of a demographic definition of electoral districts. Here constituents are assigned to representatives based on their ages. For example, all constituents ages 18-22 are assigned to one representative, and so on. Here the representative will need to understand the issues facing people with similar ages and varying political views. Town meetings will tend to be virtual to reach a geographically distributed constituency.

A “random assignment” approach simply assigns constituents to representatives at random. This encourages each representative to understand and consider a diverse range of issues and concerns. This is a form of proportional representation, discussed below.

A “you choose” approach allows constituents to choose their preferred representative (among those elected). Constituents indicate their ranked choice preferences, and an algorithm performs a best fit match of constituents to representatives. This approach can lead to unhelpful polarization if a representative holds extreme positions and attracts many like-minded constituents.

In each case the currently assigned constituents form the electoral district for the next election.

The goal is to increase accurate representation of the people, reduce political polarization, reduce political gridlock, and improve politician’s focus on solving problems faced by their constituents.

Mathematician Jordan Ellenberg has studied this issue in depth.[1] One approach is to require districts to have compact “reasonable shapes” rather than the extensive and jagged shapes often associated with gerrymandering. This notion of compactness can be expressed mathematically by calculating:

area / perimeter2

for each district. This ratio (when multiplied by 4π) is called the Polsby-Popper score. This method was chosen by Arizona's redistricting commission in 2000. While this measure may be aesthetically appealing, it is still possible to draw partisan maps with a high Polsby-Popper score.

Another approach is proportional representation. Proportional representation is the principle that each party ought to get a share of seats in the legislature equal to the proportion of the popular vote drawn by the candidates. While this may sound fair, it can be quite unfair. Consider an example where 60% of the voters favor a particular party. If the stare were divided into 10 districts each with proportional representation, then each of those districts would have voters representing 60% for the majority party. This leaves the minority party with no representative districts.

Another approach is to reduce the number of wasted votes—votes cast that do not help to elect a candidate—by reducing the efficiency gap. Unfortunately using the efficiency gap to design districts can cause significant instabilities. A map that results in a small efficiency gap for one election can result in substantial efficiency gaps for subsequent elections.

Another approach is described in the “Amicus brief of mathematicians, law professors, and students in support of appellees and affirmance”[2] , submitted to the Supreme Court March 8, 2019. The brief “presents and illustrates a computational method that is designed to efficiently produce representative samples—in this application, by sampling alternative valid districting plans. Courts can then reasonably infer the presence of intentional discrimination by assessing a given district in the context of valid alternative plans.”

The approach described is to generate a large ensemble of maps via computer algorithm, and to then compare proposed maps to the fairness of the computer-generated ensemble. This provides the “manageable standard” the court seeks for evaluating gerrymandering.

None-the-less, in Rucho v. Common Cause, a landmark 2019 case of the United States Supreme Court concerning partisan gerrymandering, the Court ruled that while partisan gerrymandering may be "incompatible with democratic principles", the federal courts cannot review such allegations, as they present nonjusticiable political questions outside the remit of these courts.

Perhaps the best approach is to have a nonpartisan commission draw the district maps.


  1. Ellenberg, Jordan. Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. Penguin Books. pp. 480. ISBN 978-1984879073.  Chapter 14.
  2. Math Brief”