Gibbard–Satterthwaite theorem
Impossibility result for ranked-choice voting systems / From Wikipedia, the free encyclopedia
The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961[1] and then proved independently by the philosopher Allan Gibbard in 1973[2] and economist Mark Satterthwaite in 1975.[3] It deals with deterministic ordinal electoral systems that choose a single winner, and shows that for every voting rule of this form, at least one of the following three things must hold:
- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
- The rule limits the possible outcomes to two alternatives only; or
- The rule is not straightforward, i.e. there is no single always-best strategy (one that does not depend on other voters' preferences or behavior).
This article needs attention from an expert in game theory. The specific problem is: inadequate description of theorem and practical importance. (June 2024) |
It has been suggested that Gibbard's theorem be merged into this article. (Discuss) Proposed since November 2023. |
Gibbard's proof of the theorem is more general and covers processes of collective decision that may not be ordinal, such as cardinal voting.[note 1] Gibbard's 1978 theorem and Hylland's theorem are even more general and extend these results to non-deterministic processes, where the outcome may depend partly on chance; the Duggan–Schwartz theorem extends these results to multiwinner electoral systems.