Voting Theory and Social Choice: Arrow's Theorem and Voting Systems

Making fair group decisions is a fundamental challenge across mathematics, economics, and computer science. This text-based course introduces you to the foundations of voting theory and social choice, providing clear frameworks to evaluate how collective preferences translate into outcomes. You will build a solid understanding of how democratic algorithms work and why perfectly fair voting systems are mathematically impossible. What you'll learn: Understand fundamental concepts of preference aggregation and voting mechanisms. Analyze classical voting systems including plurality, Borda count, Condorcet methods, and instant-runoff. Examine Arrow's Impossibility Theorem and its profound implications for democratic decision-making. Evaluate the Gibbard-Satterthwaite theorem and strategic manipulation in voting rules. Explore computational social choice concepts and modern preference ranking models. The course starts with essential definitions and voting axioms before advancing step by step through proofs, paradoxes, and algorithmic considerations. This course is designed for curious beginners, mathematics enthusiasts, and computer science students with no advanced background required. Start reading today to master the mathematical principles behind voting and collective choice.