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Revista de Matemática Teoría y Aplicaciones

versão impressa ISSN 1409-2433

Rev. Mat vol.27 no.1 San José Jan./Jun. 2020

http://dx.doi.org/10.15517/rmta.v27i1.39970 

Artículo

Modeling voting dynamics in a two-party system

Modelar la dinámica de votación en un sistema de dos partidos

Tin Phan1 

M. Gabriela Navas-Zuloaga2 

Caleb Ignace3 

Christopher M. Kribs4 

Carlos W. Castillo-Garsow5 

Victor M. Moreno6 

1Arizona State University; Department of Mathematical and Statistical Sciences; Tempe AZ; United States; Tin.T.Phan@asu.edu

2Arizona State University; Computational and Modeling Sciences Center; Tempe AZ; United States; mnavaszu@asu.edu

3Arizona State University; Department of Mathematical and Statistical Sciences; Tempe AZ; United States; cignace@asu.edu

4University of Texas at Arlington; Departments of Mathematics and Curriculum & Instruction; Arlington TX; United States; kribs@uta.edu

5Eastern Washington University; Department of Mathematics; Cheney WA; United States; ccastillogarsow@ewu.edu

6Arizona State University; Department of Mathematical and Statistical Sciences; Tempe AZ; United States; Brown University; Division of Applied Mathematics; Providence RI; United States; Victor.M.Moreno@asu.edu

Abstract

The 2016 U.S. presidential primary election, characterized by unexpected results, provides an interesting context to study how citizens are influenced in deciding whether to vote and whom to support. Our aim is to determine which of those changes in voting behavior have the largest impact on the election outcome. We address this question by developing a class of models driven either by the effect of mass media or by social interaction among voters and non-voting members of two parties. The dynamics are modeled using four compartments with a transition matrix describing the evolution of a discrete-time Markov chain. Each model is studied and fit to poll data from the 2012 and 2016 U.S. presidential elections using numericamethods. A comparison across elections indicates that the social influence of each group changes from one election to another, but response to media is similar in both cases.

Keywords: Markov chain; dynamical system; voting behavior; peer influence; media influence.

Resumen

Las elecciones presidenciales de 2016 en los E.E.U.U., caracterizadas por resultados inesperados, proveen un contexto interesante para estudiar cómo son influenciados los ciudadanos en su decisión de voto. Nuestro objetivo es determinar qué cambios en la intención de voto tienen mayor impacto en el resultado. Con este fin desarrollamos una clase de modelos basados en o (1) los medios de comunicación masivos o (2) las interacciones entre los votantes y miembros de dos partidos. Dividimos a la población en cuatro compartimientos con una matriz de transición que describe la evolución de una cadena de Markov en tiempo discreto. Estudiamos cualitativamente cada modelo y utilizamos métodos numéricos para ajustar los parámetros a datos provenientes de encuestas previas a las elecciones de 2012 y 2016. Encontramos que la influencia social en cada grupo cambia de una elección a la siguiente, pero la respuesta a los medios de comunicación es similar en ambos casos.

Palabras clave: cadena de Markov; comportamiento electoral; influencia de pares; influencia de medios de comunicación.

Mathematics Subject Classification: 91F10.

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Acknowledgements

The authors thank the Mathematical and Theoretical Biology Institute (MTBI) co-Directors Drs. Carlos Castillo-Chavez, Anuj Mubayi, and Marlio Paredes for the opportunity to conduct this research; Associate Director Sherry Woodley and Coordinator Ciera Duran for their efforts in planning and executing the day-to-day activities of MTBI; and special thanks to Drs. Daniel Burkow and Leon Arriola for their guidance and support.

This research was carried out at MTBI which is a Research Experience for Undergraduate (REU) summer program at the Simon A. Levin Mathematical, Computational and Modeling Sciences Center (SAL MCMSC) at Arizona State University (ASU). This project was partially supported by grants from the National Science Foundation (DMS1263374), the Office of the President of ASU, and the Office of the Provost at ASU.

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Received: May 12, 2019; Revised: August 14, 2019; Accepted: September 13, 2019

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