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. 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 the Khot-Vishnoi instance of Max-Cut does not provide a gap instance for the Lasserre hierarchy.
Original language | English (US) |
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Article number | 4 |
Journal | Theory of Computing |
Volume | 12 |
DOIs | |
State | Published - 2016 |
Funding
Supported by Umesh Vazirani’s Templeton Foundation Grant 21674., Supported by NSF award DMS-1106999, CCF-1320105, DOD ONR grant N000141110140 and Simons Foundation grant 328025., Supported by NSF award DMS-1106999 and DOD ONR grant N00014-11-1-0140, ONR grant N00014-14-1-0823.
Keywords
- Gaussian isoperimetry
- Majority is Stablest
- Sum-of-Squares hierarchy
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Theory and Mathematics