The Gibbard-Satterthwaite theorem states that every nondictatorial election rule among at least three alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with a nonnegligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range.
- Algorithmic game theory
- Arrow theorem
- Gibbard-Satterthwaite theorem