Dynamics of Democratic Elections: A Mathematical Approach to Political Science

Dynamics of Democratic Elections explores modeling approaches to democratic elections and opinion dynamics at the intersection of mathematics, political science, and computational modeling. The book focuses on relatively simple models, their analysis, and how they perform in real-world applications. In order to make the book easy to navigate, the material is divided into three major parts concerning ‘The Voter Model’, ‘Nonlinear Election Models’, and ‘Game Theoretical Models’. Although the material is unashamedly mathematical, the concepts are discussed in a way that should be accessible to anyone with a reasonably strong quantitative background and should prove interesting to a broad audience beyond mathematicians. Features Suitable for graduate students and researchers (mathematicians, physicists, social and political scientists with a strong theoretical background) Step-by-step data preparation and analysis Abundant exercises Numerous color illustrations

Table of Contents:
Foreword Preface Section I The Voter Model and its extensions Chapter 1 Warm up: Votes per candidate Chapter 2 The voter model Chapter 3 The zealot Model Chapter 4 The Voter Model with Party Dynamics Section II Nonlinear election models Chapter 5 Elections and the Potts model Chapter 6 Reinforcement Model Chapter 7 Unifying ground of the Potts and the Voter model Chapter 8 Hierarchical models Section III Rational voting - Game theoretical models Chapter 9 Spatial valence model Chapter 10 Voting paradox Appendix A Dynamical systems in a nutshell Appendix B Stochastic models in a nutshell Appendix C Voter Model with Party Dynamics – details Appendix D Appendix: Tables for chapter 7 Bibliography Appendix E Data sources

About the Author :
Johannes Müller is an associate professor of mathematics at the Technische Universität München. His work bridges mathematics with the life and social sciences, focusing on dynamical systems and stochastic processes. Key areas of application include epidemiology – especially vaccination strategies and contact tracing – cell regulatory pathways with an emphasis on quorum sensing, and population genetics, including the role of quiescence. In the social sciences, his research explores elections, opinion dynamics, and social interaction models. Johannes studied in Karlsruhe and Tübingen, where he completed his habilitation in 2001. Following stays in Utrecht and Cologne, he led a research group at the Helmholtz Center in Munich before joining TUM in 2004. Volker Hösel studied physics and mathematics at the University of Erlangen-Nuremberg, earning both degrees with distinction. He completed his Ph.D. in stochastic processes and habilitation in mathematics at the Technical University of Munich. His academic career includes research at the GSF Research Center for Environment and Health, a sabbatical at the University of North Carolina at Chapel Hill, and extensive teaching at the Technical University of Munich. Dr. Hösel specializes in applied statistics, bioinformatics, and functional analysis. He lives and works in Munich, Germany. Aurélien Tellier is a theoretical evolutionary biologist. Aurélien studied agronomy, plant biology, genetics, and statistics at ENITA (Bordeaux, France) and population genetics at AgroParisTech Paris, France). After obtaining his doctorate at the John Innes Centre (Norwich, UK) in 2007, he spent five years as a postdoctoral research fellow at LMU Munich. Since 2012, he has held the position of associate professor of population genetics at the Technical University of Munich. Aurélien’s area of research is to develop population genetics theoretical models to comprehend genome evolution at the population or species level, aiming to bridge evolutionary and ecological time scales and processes. He also explores the evolutionary mechanisms of plant adaptation to their environment, considering aspects such as different climatic conditions and resistance against parasites (bacteria, fungi, insects). The primary focus of his research is the study of plant-parasite coevolution and long-term seed dormancy in the soil. Besides biology, Aurelien is interested in assessing the importance of random processes for disease epidemiology or human choices (for example in politics). Christoph Mohamad-Klotzbach studied Political Science, Sociology, and History at the University of Würzburg. In his PhD thesis, he developed a new approach for measuring cleavage structures in democracies. He is currently a Post-Doctoral Researcher in Comparative Politics at the Institute of Political Science and Sociology at the University of Würzburg, Germany. His research areas are Political Culture, Democracy Studies, Stateness, Political Parties and Voting Behaviour. Between 2019 and 2023 he was the coordinator of the interdisciplinary DFG research group FOR2757 on “Local self-regulation in the context of weak statehood between antiquity and modernity (LoSAM)” and between 2018 and 2024 he was a speaker of the Working Group on Democracy Studies in the German Political Science Association (DVPW). He was a guest researcher at Canterbury Christ Church University in Kent, at the IESP-UERJ in Rio de Janeiro and at the UFRGS in Porto Alegre.