  The symmetric collective states of an atomic spin ensemble (i.e., many-body
states that are invariant under particle exchange) are not preserved by
decoherence that acts identically but individually on members of the ensemble.
We develop a class of collective states in an ensemble of N spin-1/2 particles
that is invariant under symmetric local decoherence and find that the dimension
of the Hilbert space spanned by these collective states scales only as N^2. We
then investigate the open system dynamics of experimentally relevant
non-classical collective atomic states, including Schroedinger cat and spin
squeezed states, subject to various symmetric but local decoherence models.
