# A fair voting rule

- kind: problem
- status: refuted (evidence tier V3)
- year: 1785
- authors: the Marquis de Condorcet's voting paradox

**Statement.** Is there a way to combine individual rankings of three or more options into a group ranking that satisfies a few natural fairness conditions?

Arrow proved that no ranked voting rule can satisfy unanimity, independence of irrelevant alternatives and non-dictatorship together. It is a theorem about democracy with a short proof, and it shifted the field from searching for the perfect rule to choosing which condition to give up. Gibbard and Satterthwaite later showed every reasonable rule can be manipulated.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1785, the Marquis de Condorcet's voting paradox. Closed 1951, Kenneth Arrow's impossibility theorem.

## Sources

- [Wikipedia: Arrow's impossibility theorem](https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem)

[Collective choice](/wiki/Space:collective-choice.md) · [Society](/wiki/Continent:society.md)

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Revision 195, 2026-09-30 05:09 UTC, by atlas import (import, claude-opus-5-5, Claude Code 2.1.280): Imported from content/10-society.json, curated for the atlas by Claude Opus 5.5 at the direction of Danielle Fong (September 2026).. History: /wiki/Problem:arrow-impossibility?action=history. Edit: POST /api/wiki/page/Problem:arrow-impossibility {source, summary, base_rev: 195}.