The Mathematics of Democracy, Politics and Manipulation

Welcome to The Mathematics of Politics, Democracy, and Manipulation, an inspiring course that explores the intricate landscape of democracy and decision-making. In today's world, understanding the mechanisms that shape our electoral systems and influence democratic outcomes is more crucial than ever. This comprehensive course delves deep into five key pillars of electoral theory and practice, empowering participants with the knowledge and tools to navigate the complexities of voting and representation. Voting Theory: Discover the theoretical foundations of voting systems, from classic methods like plurality voting to innovative approaches such as ranked-choice and approval voting. Explore the principles of fairness, efficiency, and representation that underpin different voting methods, and gain insights into their real-world applications and implications. US Electoral College: Journey through the history, mechanics, and controversies of the United States Electoral College. Unravel the mysteries of presidential elections, from the allocation of electoral votes to the winner-takes-all system, and examine the impact of the Electoral College on American politics and governance. Weighted Voting: Unlock the secrets of weighted voting systems and their role in decision-making. From corporate boards to international organizations, explore how weighted voting structures allocate power and influence, and learn how to analyze and evaluate the distribution of voting power within diverse coalitions. Apportionment: Delve into the principles and practices of apportionment, the process of allocating political representation. Examine the challenges of balancing population equality, geographic representation, and minority rights, and explore the methodologies used to divide legislative seats in democratic societies. Gerrymandering: Confront the complexities and controversies of electoral boundary manipulation. Investigate the tactics and consequences of gerrymandering, from partisan bias to minority vote dilution, and explore strategies for promoting fairness, transparency, and integrity in electoral processes. Through engaging lectures, interactive discussions, and hands-on exercises, participants will develop a deep understanding of voting theory, electoral processes, and the challenges facing modern democracies. Whether you're a student, a policymaker, or a concerned citizen, join us on this transformative journey as we work towards a more inclusive, equitable, and vibrant democracy for all.

• Introduction to Voting Theory
• Voting theory is the fascinating study of how societies make collective decisions. Whether it's electing a political leader, selecting the best option in a group decision, or determining fair allocations of resources, understanding voting mechanisms is essential for anyone interested in governance, social dynamics, or even game theory. In this module, we delve into the rich landscape of voting theory, uncovering the complexities behind seemingly simple processes. From the classic plurality voting to more intricate systems like ranked-choice voting and approval voting, we explore the strengths, weaknesses, and implications of each method.
• Other Voting Methods and Criteria
• While the plurality voting system is the most widely used method in many elections, it's only one piece of the puzzle. In this module, we'll venture into the realm of alternative voting methods, where the choices are not limited to a single candidate or option. This journey beyond the world of Plurality will take us into the diverse world of democratic decision-making. Voting is not just about selecting the most popular candidate; it's about accurately reflecting the will of the electorate, ensuring representation for diverse viewpoints, and promoting a fair and inclusive decision-making process. To achieve these goals, various alternative voting methods have been devised, each with its own strengths and weaknesses. Throughout this module, we'll examine the principles, mechanics, and implications of each voting method, considering their suitability for different contexts and their potential to address common challenges
• The Complexities of Voting
• In this module, we venture into the heart of democratic theory to confront one of its most perplexing puzzles. In the realm of collective decision-making, democracy stands as a beacon of hope, promising to reflect the will of the people and promote societal harmony. Yet, beneath this noble facade lies a labyrinth of complexity, where competing values, preferences, and ideals collide. This module introduces Arrow's Impossibility Theorem, a seminal work by Nobel laureate Kenneth Arrow that shakes the very foundation of democratic theory. This theorem boldly proclaims that no voting system can satisfy a set of minimal fairness criteria simultaneously, rendering the quest for a perfect electoral method akin to chasing a mirage in the desert. By confronting Arrow's Impossibility Theorem head-on, you will not only gain a deeper understanding of the inherent complexities of democracy but also emerge with newfound insights into the possibilities and limitations of collective decision-making. Whether you're a student of political science, a passionate advocate for social change, or simply a curious mind eager to explore the frontiers of democratic theory, this module will help you navigate the turbulent seas of democracy's first big enigma.
• Weighted Voting Systems
• In democratic societies and organizational settings alike, decisions are rarely made on a purely egalitarian basis. Instead, individuals and entities often wield varying degrees of influence, shaped by factors such as wealth, resources, or strategic alliances. This module introduces you to the the mechanics of weighted voting systems and a measurement of power, called Banzhaf power, that offers a key to decoding complexities in a weighted voting system.
• Shapley-Shubik Power Index
• In any group or organization, understanding who holds sway over decisions and why is crucial for navigating complex social and political landscapes. Along with the Banzhaf Power Index, this module introduces you to the Shapley-Shubik power index - a powerful lens through which to analyze and quantify the relative influence of individual players in a weighted setting. By uncovering the hidden dynamics of power, you will develop a nuanced understanding of decision-making dynamics in complex environments.
• The United States Electoral College
• In this module, we will introduce the US Electoral College as a weighted voting systems and using our tools of Banzhaf and Shapley-Shubik Power Indices, we will demystify one of the cornerstone institutions of American democracy. The United States Electoral College has been a subject of both fascination and controversy since its inception. In this module, we embark on a journey to unravel the intricacies of the Electoral College system, exploring its history, mechanics, and impact on the American political landscape. By the end of this module, you will not only have a deep understanding of the US Electoral College but also the tools to critically evaluate its strengths, weaknesses, and potential for reform. Whether you're a student of political science, a concerned citizen, or simply curious about the intricacies of American democracy, join us on this enlightening journey as we decode the mysteries of the Electoral College.
• Apportionment
• In democratic societies, the fair and equitable distribution of representation is fundamental to ensuring that all voices are heard and all communities are adequately represented. Apportionment, the process of dividing seats in a legislative body among different geographic areas or population groups, lies at the heart of this endeavor. This module is designed to introduce you to the the process of turning the Census results into representation for the House. Like voting theory, there is more here than you might initially expect. In this module, we delve into the complex and essential process of allocating political representation. By the end of this module, you will not only have a deep understanding of the principles and practices of apportionment but also the tools to critically evaluate apportionment methods and advocate for fair and effective representation in your communities and beyond.
• Gerrymandering
• Welcome to a module dedicated to shedding light on one of the most contentious issues in modern politics: gerrymandering. Gerrymandering, the practice of manipulating electoral district boundaries to favor one political party or group, strikes at the heart of democratic principles. In this module, we embark on a journey to explore the origins, mechanics, and consequences of gerrymandering, and examine strategies for promoting fair and equitable representation. Additional Reading and References for this constantly changing section include: 1. Political Geometry Rethinking Redistricting in the US with Math, Law, and Everything In Between, by Duchin, Walch (ed), Springer, 2022 (https://link.springer.com/book/10.1007/978-3-319-69161-9) 2. The Mathematics of Voting and Elections: A Hands-on Approach: Second Edition (Mathematical World), 2 ed., by Jonathan K. Hodge, Richard E. Klima 3. Gerrymandering in America: The House of Representatives, the Supreme Court, and the Future of Popular Sovereignty by Anthony J. McGann, Charles Anthony Smith , et al. | Apr 4, 2016