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

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

2011-05-25

arxiv.org/abs/1105.5129v1

Mathematics

Combinatorics

27 pages, extended version of a FOCS'08 paper, to appear in SICOMP

Scientific paper

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 non-negligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range.

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