Majority is stablest: Discrete and SoS

Anindya De, Elchanan Mossel, Joe Neeman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Scopus citations


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. The new proof is general enough to include all previous variants of majority is stablest such as "it ain't over until it's over" and "Majority is most predictable". 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 Khot-Vishnoi instance of Max-Cut does not provide a gap instance for the Lasserre hierarchy.

Original languageEnglish (US)
Title of host publicationSTOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing
Number of pages10
StatePublished - Jul 11 2013
Event45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States
Duration: Jun 1 2013Jun 4 2013


Other45th Annual ACM Symposium on Theory of Computing, STOC 2013
Country/TerritoryUnited States
CityPalo Alto, CA


  • Majority is stablest
  • Sum of squares hierarchy
  • Unique games conjecture

ASJC Scopus subject areas

  • Software


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