A Counterexample to the "Majority is Least Stable" Conjecture

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.

💡 Research Summary

The paper presents a concrete counterexample to the “Majority is Least Stable” conjecture originally posed by Benjamini, Kalai, and Schramm. The conjecture asserts that for any odd number of Boolean variables n, every linear threshold function (LTF) f :{−1,1}ⁿ → {−1,1} should have noise stability at least as large as that of the majority function Majₙ, for every correlation parameter ρ∈