Mathematical Modeling of U.S. Elections
Adviser: Alexandria Volkening
Subject: Applied 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.