  We prove the three candidate Plurality is Stablest Conjecture of
Khot-Kindler-Mossel-O'Donnell from 2005 for correlations $\rho$ satisfying
$-1/43<\rho<1/10$: the Plurality function is the most noise stable three
candidate election method with small influences, when the corrupted votes have
correlation $-1/43<\rho<1/10$ with the original votes. The previous best result
of this type only achieved positive correlations at most $10^{-10^{10}}$. Our
result follows by solving the three set Standard Simplex Conjecture of
Isaksson-Mossel from 2011 for all correlations $-1/43<\rho<1/10$.
  The Gaussian Double Bubble Theorem corresponds to the case $\rho\to1^{-}$, so
in some sense, our result is a generalization of the Gaussian Double Bubble
Theorem. Our result is also notable since it is the first result for any
$\rho<0$, which is the only relevant case for computational hardness of
MAX-3-CUT. In fact, assuming the Unique Games Conjecture, we show that
MAX-3-CUT is NP-hard to approximate within a multiplicative factor of $.98937$,
which improves on the known (unconditional) NP-hardness of approximation within
a factor of $1-(1/102)$, proven in 1997. As an additional corollary, we
conclude that three candidate Borda Count is stablest for all
$-1/43<\rho<1/10$.
