Voting Paradoxes

Condorcet and Arrow

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A Condorcet winner beats every rival head-to-head, but may not exist.
• Majority preferences can form cycles (Condorcet’s paradox).
• Arrow: no ranked method with 3+ candidates meets all the fairness conditions.

Steps

1. Head-to-head
2. Rock, paper, scissors
3. Arrow’s impossibility theorem
4. All the contests
5. Find the spoiler
6. The spoiler effect