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Gaussian noise stability results have recently played an important role inproving results in hardness of approximation in computer science and in thestudy of voting schemes in social choice. We prove a new Gaussian noisestability result generalizing an isoperimetric result by Borell on the heatkernel and derive as applications:  * An optimality result for majority in the context of Condorcet voting.  * A proof of a conjecture on "cosmic coin tossing" for low influencefunctions.  We also discuss a Gaussian noise stability conjecture which may be viewed asa generalization of the "Double Bubble" theorem and show that it implies:  * A proof of the "Plurality is Stablest Conjecture".  * That the Frieze-Jerrum SDP for MAX-q-CUT achieves the optimal approximationfactor assuming the Unique Games Conjecture.

Maximally stable Gaussian partitions with discrete applications