Untitled

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.

Untitled

“…The proof of the theorem, which is omitted, is by now a standard reduction from a Gaussian noise stability result to a discrete one [25,17,6]. In one direction, the invariance principle immediately bounds the discrete stability of any partition by the Gaussian stability.…”