, Volume 35, Issue 3, pp 317–387 | Cite as

A quantitative Gibbard-Satterthwaite theorem without neutrality

  • Elchanan MosselEmail author
  • Miklós Z. Rácz
Original Paper


Recently, quantitative versions of the Gibbard-Satterthwaite theorem were proven for k=3 alternatives by Friedgut, Kalai, Keller and Nisan and for neutral functions on k ≥ 4 alternatives by Isaksson, Kindler and Mossel.

We prove a quantitative version of the Gibbard-Satterthwaite theorem for general social choice functions for any number k ≥ 3 of alternatives. In particular we show that for a social choice function f on k ≥ 3 alternatives and n voters, which is ε-far from the family of nonmanipulable functions, a uniformly chosen voter profile is manipulable with probability at least inverse polynomial in n, k, and ε −1.

Ours is a unified proof which in particular covers all previous cases established before. The proof crucially uses reverse hypercontractivity in addition to several ideas from the two previous proofs. Much of the work is devoted to understanding functions of a single voter, and in particular we also prove a quantitative Gibbard-Satterthwaite theorem for one voter.

Mathematics Subject Classification (2000)



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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.University of CaliforniaBerkeleyUSA

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