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

Three Candidate Plurality is Stablest for Correlations at most 1/10