Logic of Voting: When Math Meets Democracy

• Event: LIMIT Camp 2024, Category A
• Organiser: LIMIT
• Venue: Online (via Google Meet)
• Date: 12 June, 2025
• Abstract: Voting is the cornerstone of democratic decision-making, yet the process of translating individual preferences into a collective choice is far from straightforward. In this talk, we will explore the mathematical foundations of voting systems, examining how different methods—plurality, ranked-choice, and others—attempt to achieve fairness while navigating inherent paradoxes. As we delve deeper, we will encounter Arrow’s Impossibility Theorem, a profound result that reveals the fundamental limitations of any voting system striving to satisfy a set of reasonable fairness criteria. Through this journey, we will uncover the intricate logic that governs democratic processes, gaining insight into why no perfect voting system exists and how mathematics shapes the way societies make collective decisions.