  The Standard Simplex Conjecture and the Plurality is Stablest Conjecture are
two conjectures stating that certain partitions are optimal with respect to
Gaussian and discrete noise stability respectively. These two conjectures are
natural generalizations of the Gaussian noise stability result by Borell (1985)
and the Majority is Stablest Theorem (2004). Here we show that the standard
simplex is not the most stable partition in Gaussian space and that Plurality
is not the most stable low influence partition in discrete space for every
number of parts $k \geq 3$, for every value $\rho \neq 0$ of the noise and for
every prescribed measures for the different parts as long as they are not all
equal to $1/k$. Our results do not contradict the original statements of the
Plurality is Stablest and Standard Simplex Conjectures in their original
statements concerning partitions to sets of equal measure. However, they
indicate that if these conjectures are true, their veracity and their proofs
will crucially rely on assuming that the sets are of equal measures, in stark
contrast to Borell's result, the Majority is Stablest Theorem and many other
results in isoperimetric theory. Given our results it is natural to ask for
(conjectured) partitions achieving the optimum noise stability.
