An Application of Differential Equations to Political Partisanship — Presentation Detail — Celebration of Scholars

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Jun Wang
Kim Instenes
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James Ripley

An Application of Differential Equations to Political Partisanship

Name: Alyssa Miller
Major: Mathematics
Hometown: Maplewood, MN
Faculty Sponsor: Mark Snavely
Other Sponsors:
Type of research: Senior thesis

Abstract

The current political climate suggests an overarching decrease in political partisanship in the United States, which could have serious implications in the political sphere. To test this theory, we consider a differential equations model applicable for scenarios involving two group competition that can be used to translate actual data into projected future outcomes. First, we consider the model generally by addressing the stability of all possible equilibrium points. Then, using Gallup Poll data on United States political partisanship versus non partisanship, we find parameters for the model that form a least-squares best fit, utilizing Mathematica programming to solve the differential equation for optimal parameter values. Finally, we use the model to project the trend towards or away from party identity, and determine whether it seems as though an eventual steady state will emerge. Three data samples are analyzed: 2004 through 2013, 2012 until the presidential election, and post 2012 election through 2013. We find that conclusions regarding eventual steady states vary between data sets, but values for the parameters elicit thought provoking questions regarding political party affiliation.

Poster file