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

Authors:
Ehud Friedgut;Gil Kalai;Nathan Keller;Noam Nisan
Affiliations:
ehudf@math.huji.ac.il and noam.nisan@gmail.com;kalai@math.huji.ac.il;nathan.keller@weizmann.ac.il;-
Venue:
SIAM Journal on Computing
Year:
2011

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Abstract

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.