Mathematical Modeling of U.S. Elections

Jun 13, 2020 | NURJ x EXPO 2020 Poster

William He

William He is an undergraduate student studying Applied Mathematics at Northwestern University’s McCormick School of Engineering and is set to graduate in 2023. He also has interests in Computer Science and Statistics, and would like to pursue a career related to mathematical modeling. In that regard, this research project is the first he has been involved in, and he will continue collaborating on it to forecast the 2020 presidential elections. At Northwestern, William is also a Murphy Scholar and a member of the Investment Management Group’s Portfolio Committee, where he evaluates investment positions on various US equities.

Christopher Lee

Christopher Lee is a rising Sophomore undergraduate student studying Applied Mathematics in the McCormick School of Engineering. He plans to pursue Applied Mathematics with a focus in computer science and data analysis. Christopher’s research experience with election forecasting involves the areas of data handling, parameter fitting and programming. This fits well with his academic experience focusing on mathematics and computer science through the introductory engineering coursework. He will continue his work with Will this summer by applying the model to the upcoming 2020 elections. When he’s not coding, Christopher enjoys playing frisbee for the Northwestern Ultimate Team and hanging out with friends.


AdviserAlexandria Volkening
SubjectApplied Math

Forecasting the outcomes of U.S. elections is a relevant and complex task that has been approached in many ways, most commonly incorporating statistics or proprietary methods that include some degree of subjectivity. Our approach differs from this convention in that we use multidisciplinary methods from applied mathematics. Specifically, we use a system of differential equations commonly employed for the study of disease transmission, to model the spread of political affiliation (Democrat or Republican) across states. We apply these models through programs written in R for data analysis and MATLAB for simulations. We are able to run thousands of simulations, with the addition of noise to account for uncertainty, to make a range of forecasts for election outcomes at the state level, specifically focused on swing states. The model’s forecasts for past presidential, senatorial, and gubernatorial elections after 2012 have accuracy comparable to popular forecasting sites. In this project, we are working to test the accuracy of the model with the 2004 and 2008 presidential elections. Our work demonstrates the effectiveness of data-driven forecasting from a mathematical modeling perspective and suggests additional research in this field.