## 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.

Original language | English (US) |
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Title of host publication | STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing |

Pages | 477-486 |

Number of pages | 10 |

DOIs | |

State | Published - Jul 11 2013 |

Event | 45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States Duration: Jun 1 2013 → Jun 4 2013 |

### Other

Other | 45th Annual ACM Symposium on Theory of Computing, STOC 2013 |
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Country | United States |

City | Palo Alto, CA |

Period | 6/1/13 → 6/4/13 |

## Keywords

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

## ASJC Scopus subject areas

- Software