  I propose that self-duality in quantum phase-space provides the criteria for
the selection of the quantum gravity vacuum. The evidence for this assertion
arises from two independent considerations. The first is the phenomenological
success of the free fermionic heterotic-string models, which are constructed in
the vicinity of the self-dual point under T-duality. The relation between the
free fermionic models and the underlying Z2 X Z2 toroidal orbifolds is
discussed. Recent analysis revealed that the Z2 X Z2 free fermionic orbifolds
utilize an asymmetric shift in the reduction to three generations, which
indicates that the untwisted geometrical moduli are fixed near the self-dual
point. The second consideration arises from the recent formulation of quantum
mechanics from an equivalence postulate and its relation to phase-space
duality. In this context it is demonstrated that the trivial state, with
V(q)=E=0, is identified with the self-dual state under phase-space duality.
These observations suggest a more general mathematical principle in operation.
In physical systems that exhibit a duality structure, the self-dual states
under the given duality transformations correspond to critical points.
