A Quantitative Version of the Gibbard-Satterthwaite Theorem for Three Alternatives

The Gibbard-Satterthwaite theorem states that every non-dictatorial 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.

• Type: Journal
• Year: 2011
• Where: SIAMCOMP
• Authors: Ehud Friedgut, Gil Kalai, Nathan Keller, Noam Nisan
• Keywords: Formal Methods, Gibbard, Quantitative Version, SIAMCOMP 2011, Theorem States