Gibbard–Satterthwaite theorem

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 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975, which shows that all ranked-choice voting systems are vulnerable to manipulation by strategic voting.

The theorem does not apply to cardinal voting systems such as score voting or STAR voting nor does it apply to decision mechanisms other than ranked-choice voting. Gibbard's theorem provides a weaker result that applies to such mechanisms.

The Gibbard-Satterthwaite theorem is often misunderstood as claiming that "every voting system encourages dishonesty" or the related adage that "there is no best voting system." However, such interpretations are not correct; by the revelation principle, there exist many (deterministic, non-trivial) voting systems that allow for honest disclosure (outside the class of ranked-choice voting systems).