research-article

Majority is stablest: discrete and SoS

Authors:

Elchanan Mossel,

Joe NeemanAuthors Info & Claims

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

Pages 477 - 486

https://doi.org/10.1145/2488608.2488668

Published: 01 June 2013 Publication History

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.

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Cited By

Mossel E(2021)Probabilistic view of voting, paradoxes, and manipulationBulletin of the American Mathematical Society10.1090/bull/175159:3(297-330)Online publication date: 2-Dec-2021
https://doi.org/10.1090/bull/1751
Filmus YKindler GMossel EWimmer K(2018)Invariance Principle on the SliceACM Transactions on Computation Theory10.1145/318659010:3(1-37)Online publication date: 13-Apr-2018
https://dl.acm.org/doi/10.1145/3186590
Hopkins SKothari PPotechin ARaghavendra PSchramm T(2018)On the Integrality Gap of Degree-4 Sum of Squares for Planted CliqueACM Transactions on Algorithms10.1145/317853814:3(1-31)Online publication date: 16-Jun-2018
https://dl.acm.org/doi/10.1145/3178538
Show More Cited By

Index Terms

Majority is stablest: discrete and SoS
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

June 2013

998 pages

ISBN:9781450320290

DOI:10.1145/2488608

General Chairs:
Dan Boneh
Stanford University, USA
,
Tim Roughgarden
Stanford University, USA
,
Program Chair:
Joan Feigenbaum
Yale University, USA

Copyright © 2013 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 June 2013

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STOC'13: Symposium on Theory of Computing

June 1 - 4, 2013

California, Palo Alto, USA

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STOC '13 Paper Acceptance Rate 100 of 360 submissions, 28%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Mossel E(2021)Probabilistic view of voting, paradoxes, and manipulationBulletin of the American Mathematical Society10.1090/bull/175159:3(297-330)Online publication date: 2-Dec-2021
https://doi.org/10.1090/bull/1751
Filmus YKindler GMossel EWimmer K(2018)Invariance Principle on the SliceACM Transactions on Computation Theory10.1145/318659010:3(1-37)Online publication date: 13-Apr-2018
https://dl.acm.org/doi/10.1145/3186590
Hopkins SKothari PPotechin ARaghavendra PSchramm T(2018)On the Integrality Gap of Degree-4 Sum of Squares for Planted CliqueACM Transactions on Algorithms10.1145/317853814:3(1-31)Online publication date: 16-Jun-2018
https://dl.acm.org/doi/10.1145/3178538
Dell HKim ELampis MMitsou VMömke T(2017)Complexity and Approximability of Parameterized MAX-CSPsAlgorithmica10.1007/s00453-017-0310-879:1(230-250)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s00453-017-0310-8
Hopkins SKothari PPotechin ARaghavendra PSchramm T(2016)On the integrality gap of degree-4 sum of squares for planted cliqueProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884511(1079-1095)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884511
Kauers MO'Donnell RTan LZhou YChekuri C(2014)Hypercontractive inequalities via SOS, and the Frankl-Rödl graphProceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/2634074.2634193(1644-1658)Online publication date: 5-Jan-2014
https://dl.acm.org/doi/10.5555/2634074.2634193
Xiang XHuang XZhang XCai CYang JLi L(2014)Many Can Work Better than the Best: Diagnosing with Medical Images via CrowdsourcingEntropy10.3390/e1607386616:7(3866-3877)Online publication date: 14-Jul-2014
https://doi.org/10.3390/e16073866

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