The Gibbard-Satterthwaite Theorem states that for any voting rule choosing among three or more candidates that is not dictatorial, there exist circumstances in which some voter can obtain a better outcome for themselves by misrepresenting their true preferences. Proved independently by Allan Gibbard and Mark Satterthwaite, it is a close relative of Arrow's Impossibility Theorem, showing that strategic voting cannot be entirely eliminated from any reasonable voting system.
Facts
StatementFor any deterministic voting rule with at least three possible outcomes that always selects a single winner, the rule is either dictatorial, restricts the possible outcomes to two alternatives, or is manipulable, meaning some voter can obtain a preferred outcome by misrepresenting their true preference. Allan Gibbard proved the result in 1973 and Mark Satterthwaite proved it independently in 1975. 2 Proof YearGibbard proved the theorem independently in 1973. Satterthwaite proved the same result independently in 1975, per the same source. Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Wikipedia: Gibbard-Satterthwaite theorem
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The old interpretation views it as a proof that "democracy is impossible", stating that if we require a voting rule to yield a single winner, there are distributions of voter preferences where the rule is dictatorial or "allows manipulation".
2. Gibbard-Satterthwaite Theorem (Wikipedia)
Wikimedia Foundationlead section, first paragraphQuote, lead section, first paragraph
The Gibbard-Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975.
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