Majority is stablest: Discrete and SoS

Anindya De, Elchanan Mossel, Joe Neeman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The “Majority is Stablest” Theorem has numerous applications in hardness of approximation and social choice theory. We give a new proof of the “Majority is Stablest” Theorem by induction on the dimension of the discrete cube. Unlike the previous proof, it uses neither the “invariance principle” nor Borell’s result in Gaussian space. Moreover, the new proof allows us to derive a proof of “Majority is Stablest” in a constant level of the Sum of Squares hierarchy. This implies in particular that the Khot-Vishnoi instance of Max-Cut does not provide a gap instance for the Lasserre hierarchy.

Original languageEnglish (US)
Article number4
JournalTheory of Computing
Volume12
DOIs
StatePublished - 2016

Keywords

  • Gaussian isoperimetry
  • Majority is Stablest
  • Sum-of-Squares hierarchy

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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