  Gaussian noise stability results have recently played an important role in
proving results in hardness of approximation in computer science and in the
study of voting schemes in social choice. We prove a new Gaussian noise
stability result generalizing an isoperimetric result by Borell on the heat
kernel 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 influence
functions.
  We also discuss a Gaussian noise stability conjecture which may be viewed as
a 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 approximation
factor assuming the Unique Games Conjecture.
