On The "Majority is Least Stable" Conjecture

TL;DR

This paper investigates the 'majority is least stable' conjecture, confirming its validity for small cases and disproving it for larger odd numbers, thus clarifying the conjecture's limitations.

Contribution

The paper provides a rigorous analysis of the conjecture, establishing its truth for n=1 and 3, and demonstrating its falsehood for all odd n ≥ 5.

Findings

Conjecture holds for n=1 and 3.

Conjecture is false for all odd n ≥ 5.

Results clarify the limits of the conjecture's applicability.

Abstract

We show that the "majority is least stable" conjecture is true for $n=1$ and $3$ and false for all odd $n\geq 5$.