Overview
Three voters, three candidates, no ties — and no winner. Majority rule can prefer A to B, B to C and C to A all at once.
How to solve The Voting Paradox
- Run all three head-to-head matchups instead of counting first places.
- A beats B 2–1, B beats C 2–1, and C beats A 2–1.
- The three results form a cycle, so no candidate beats every other — there is no Condorcet winner.
The key insight
Each voter's own ranking is perfectly transitive. Transitivity is simply not preserved by majority aggregation — a collective 'preference' need not behave like a preference at all.
Variations & echoes
- Arrow's impossibility theorem generalises the damage: no ranked voting rule can satisfy a short list of obviously fair conditions at once.
- Because the cycle exists, the voting ORDER decides the outcome — which is why agenda-setting is real power in committees.
Frequently asked questions
Does this mean voting is pointless?
No — it means every rule makes trade-offs. Cycles are possible, not guaranteed, and knowing which pathologies a method admits is how you choose one honestly.