Condorcet Cycle
A beats B, B beats C, yet C beats A. Majority rule therefore has no single transitive social ranking.
Condorcet & Voting Paradox Lab
Condorcet winner—
Pairwise contests0
Cycle?—
Pairwise results
How this teaches game theory
Complete scenario, mode, and level guide
Condorcet analysis compares candidates head-to-head. Collective majority preferences can be cyclic even when every voter has a perfectly consistent ranking.
Condorcet Winner
One candidate defeats every rival in direct pairwise comparison.
Agenda Manipulation
When preferences cycle, the order in which pairwise votes are held can change the final winner.
Modes and levels
Human Sets Ballot
Your ranking is inserted into the electorate so you can test whether one ballot changes pairwise outcomes.
Human vs Computer Electorate
Your ballot competes with a generated electorate, highlighting pivotal voting.
Computer Simulation
Profiles are generated automatically to search for winners and cycles.
Level 1
Three voters and three candidates expose the classic Condorcet cycle cleanly.
Level 2
More voters and a fourth candidate create richer pairwise structures.
Level 3
Random profiles show that paradoxes are structural possibilities, not one hand-crafted example.
Important: a Condorcet winner is defined by pairwise victories. It need not be the same candidate chosen by plurality, Borda count, or approval voting.