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

Marcus Isaksson*, Guy Kindeler, Elchanan Mossel

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

19 Scopus citations

Abstract

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 10-42n-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.

Original languageAmerican English
Title of host publicationProceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
PublisherIEEE Computer Society
Pages319-328
Number of pages10
ISBN (Print)9780769542447
DOIs
StatePublished - 2010
Event2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, NV, United States
Duration: 23 Oct 201026 Oct 2010

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Country/TerritoryUnited States
CityLas Vegas, NV
Period23/10/1026/10/10

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