Mathematical Modeling of the U.S. Supreme Court

The US Supreme Court has tremendous power in shaping American politics and society at large. Because justices have lifetime appointments, it is politically advantageous to ensure that a party or ideology is the majority in the court for a long period of time. This can be accomplished by appointing as many justices as possible while one political party has a unified majority — a phenomenon known as court-packing. There have been many different proposals of strategies for appointing and retiring justices and increasing the size of the court to increase the "fairness", i.e., the resistance to court-packing or ideological polarization. However, none of these proposals have been implemented in recent times; the Supreme Court as we know it (with 9 justices and lifetime appointments) has existed since 1869. There have been studies considering models that (1) consider how the ideologies of justices change over time and (2) how replacement strategies affect the ideology of the court, but considering both of these ideas together is an open question.

This project will examine the influence that the size of the court and appointment/replacement strategies have on the sensitivity of the court to court-packing. We plan on accomplishing this with the following objectives:

  • Develop statistical and dynamical models of the Supreme Court
    • Develop dynamical models for how justices on a given court influence each other.
    • Develop statistical models to simulate appointment/replacement.
    • Combine these models to simulate the court over time.
  • Examine how court size and different strategies of appointment/replacement affect the changes in ideology.
    • Examine how different strategies such as term limits, age limits, or lottery systems affect the sensitivity to court-packing.
    • Consider how stable different court sizes are to court-packing.
    • Propose different strategies to transition between court sizes and appointment/retirement policies.
  • Evaluate the philosophies and assumptions in quantitative measures of court "fairness".
    • What is an "ideal" court?
    • What influence should political parties have on the makeup/ideology of the court?
    • How to measure how "packed" a court is?

This project will be supervised in collaboration with Prof. Juan Restrepo and Ph.D. student Nicholas Landry at CU Boulder.

Essay prompt: Please address the following:

  • What interests you about this research?
  • What skills and expertise would you bring to this project?
  • What do you hope to get out of the research experience?
  • Would you potentially be interested in continuing this project beyond the spring semester (e.g., as a summer research project)?
Name of research group, project, or lab
Nonlinear & Complex Systems Research Group (in collaboration with Restrepo group at CU Boulder)
Why join this research group or lab?

You'll be working alongside a fun and supportive group of mathematicians who study a wide variety of social and biological applications. In this project, we will have the chance to tackle some interesting problems in the intersection of mathematics and politics.

This project is co-supervised and thus you will have the opportunity to work (virtually) with collaborators outside of our institution. Students may continue their work in a senior thesis, present their findings at conferences, and/or coauthor resulting publications.

Logistics Information:
Project categories
Student ranks applicable
Student qualifications
  • Required: completion of core classes in Linear Algebra and Differential Equations, programming experience (MATLAB strongly preferred)
  • Highly desirable: Math 189 Mathematics of Democracy, Probability/Statistics
  • Helpful (but not required): Dynamical Systems, Graph Theory, Operations Research, Analysis

While it is not required, preference will be given to students who have taken the Mathematics of Democracy class. Depending on interest, we may hire either one student to work individually or two students to work together in a team.

Time commitment
Spring - Part Time
Academic Credit
Number of openings
Techniques learned

A student working on this project will learn:

  • Development, analysis, and validation of mathematical models,
  • Assessing structural and political nuances and systemic impacts of the Supreme Court,
  • Numerical simulation and Monte Carlo methods for studying dynamical systems,
  • Literature reading and technical writing.
Contact Information:
Mentor name
Heather Zinn Brooks
Mentor email
Mentor position
Professor of Mathematics
Name of project director or principal investigator
Prof. Heather Zinn Brooks
Email address of project director or principal investigator
1 sp. | 0 appl.
Hours per week
Spring - Part Time
Project categories