The geometry of manipulation - A quantitative proof of the gibbard satterthwaite theorem
Paper i proceeding, 2010

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 10(-4)epsilon(2)n(-3)q(-30), where epsilon is the minimal statistical distance between f and the family of dictator functions. Our results extend those of [1], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [2], [3], [4], [5], [6]) cannot hide manipulations completely. Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies.


Marcus Isaksson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

G. Kindeler

The Hebrew University Of Jerusalem

E. Mossel

Weizmann Institute of Science Israel

University of California

2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010; Las Vegas, NV; 23 October 2010 through 26 October 2010

0272-5428 (ISSN)