C O ] 1 2 A pr 2 01 0 The Geometry of Manipulation-a Quantitative Proof of the Gibbard Satterthwaite Theorem

We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10ǫnq, where ǫ is the minimal statistical distance between f and the family of dictator functions. Our results extend those… CONTINUE READING