Mathematical Foundations of Democracy and Electoral Systems

The way a society makes collective decisions is governed by mathematical rules that can either promote fairness or enable manipulation. This course provides a clear entry point into the logic of democracy, showing how different voting systems can produce vastly different winners from the same set of preferences. You will gain a deep understanding of the structural mechanics behind elections and learn to identify when a system is vulnerable to strategic voting or unfair outcomes. * Understand the core properties of common voting methods and their mathematical strengths. * Analyze Arrow’s Impossibility Theorem and its implications for democratic stability. * Examine the mathematics of apportionment and how seats are allocated in representative bodies. * Evaluate modern voting trends, including ranked-choice systems and the logic of district drawing. * Identify mathematical paradoxes that occur in real-world political scenarios. * Apply fairness criteria to judge whether a voting system truly reflects the will of the people. Through written explanations and logical analysis, the course begins with essential terminology and the basic axioms of social choice theory before moving into detailed explorations of specific electoral models and their practical consequences. This program is designed for curious beginners who want to see the math behind the news, with no advanced mathematical background required. Start exploring the logical framework that powers modern political systems today.