A Counterexample to the "Majority is Least Stable" Conjecture

Abstract

We exhibit a linear threshold function in 5 variables with strictly smaller noise stability (for small values of the correlation parameter) than the majority function on 5 variables, thereby providing a counterexample to the "Majority is Least Stable" Conjecture of Benjamini, Kalai, and Schramm.

arXiv commentAfter this note appeared on the arXiv, we were informed that Sivakanth Gopi (in 2013), and Steven Heilman and Daniel Kane (in 2017), already independently observed that the "Majority is Least Stable" conjecture, as stated, is not true