  It is shown that $3$ disjoint sets with fixed Gaussian volumes that partition
$\mathbb{R}^{n}$ with nearly minimum total Gaussian surface area must be close
to adjacent $120$ degree sectors, when $n\geq2$. These same results hold for
any number $m\leq n+1$ of sets partitioning $\mathbb{R}^{n}$, conditional on
the solution of a finite-dimensional optimization problem (similar to the
endpoint case of the Plurality is Stablest Problem, or the Propeller Conjecture
of Khot and Naor). When $m>3$, the minimal Gaussian surface area is achieved by
the cones over a regular simplex. We therefore strengthen the Milman-Neeman
Gaussian multi bubble theorem to a "stability" statement. Consequently, we
obtain the first known dimension-independent bounds for the Plurality is
Stablest Conjecture for three candidates for a small amount of noise (and for
$m>3$ candidates, conditional on the solution of a finite-dimensional
optimization problem). In particular, we classify all stable local minima of
the Gaussian surface area of $m$ sets. We focus exclusively on
volume-preserving variations of the sets, avoiding the use of matrix-valued
partial differential inequalities. Lastly, we remove the convexity assumption
from our previous result on the minimum Gaussian surface area of a symmetric
set of fixed Gaussian volume.
