Statistics Papers

Document Type

Journal Article

Date of this Version

2013

Publication Source

Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing

Volume

STOC '13

Start Page

477

Last Page

486

DOI

10.1145/2488608.2488668

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. 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.

Comments

At the time of publication, author Elchanan Mossel was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistic Department at the University of Pennsylvania.

Keywords

majority is stablest, sum of squares hierarchy, unique games conjecture

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Date Posted: 27 November 2017

This document has been peer reviewed.