Mathematics and Democracy: Analyzing Voting and Representation

How do we ensure election outcomes truly reflect the will of the people? This text-based course introduces you to the mathematical models, theories, and algorithms that shape democratic systems worldwide. You will transition from viewing voting and representation as purely political processes to understanding them through rigorous mathematical frameworks, enabling you to analyze fairness, power dynamics, and structural biases. What you'll learn: - Learn the core principles of social choice theory and classic voting paradoxes - Analyze modern voting systems, including plurality, ranked-choice, and approval voting - Calculate voting power using mathematical indices to measure political influence - Evaluate apportionment methods used to distribute legislative seats fairly - Understand the geometry and mathematics behind redistricting and detecting gerrymandering - Apply quantitative fairness criteria to assess the integrity of democratic processes This course begins with foundational definitions of collective decision-making before guiding you step-by-step through voting algorithms, representation models, and modern spatial analysis of political districts. It is designed for curious beginners, civic-minded learners, and students of politics or math, with no advanced mathematical prerequisites required. Start reading today to uncover the hidden mathematics that governs our democratic institutions.