# A Counterexample to the "Majority is Least Stable" Conjecture

## TL;DR

This paper presents a specific counterexample in the form of a 5-variable linear threshold function that has lower noise stability than the majority function, disproving a longstanding conjecture.

## Contribution

It provides the first explicit counterexample to the 'Majority is Least Stable' Conjecture, challenging previous assumptions about noise stability in Boolean functions.

## Key findings

- Counterexample with 5 variables showing lower noise stability than majority
- Disproves the 'Majority is Least Stable' Conjecture
- Highlights limitations of previous stability conjectures

## 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.