Date of this Version
Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing
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.
majority is stablest, sum of squares hierarchy, unique games conjecture
De, A., Mossel, E., & Neeman, J. (2013). Majority Is Stablest: Discrete and SoS. Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing, STOC '13 477-486. http://dx.doi.org/10.1145/2488608.2488668
Date Posted: 27 November 2017
This document has been peer reviewed.