TY - GEN

T1 - The geometry of manipulation - A quantitative proof of the gibbard satterthwaite theorem

AU - Isaksson, Marcus

AU - Kindeler, Guy

AU - Mossel, Elchanan

PY - 2010

Y1 - 2010

N2 - 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∈2n-3q-30, where ∈ 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.

AB - 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∈2n-3q-30, where ∈ 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.

UR - http://www.scopus.com/inward/record.url?scp=78751526496&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2010.37

DO - 10.1109/FOCS.2010.37

M3 - Conference contribution

AN - SCOPUS:78751526496

SN - 9780769542447

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 319

EP - 328

BT - Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

PB - IEEE Computer Society

T2 - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010

Y2 - 23 October 2010 through 26 October 2010

ER -