  The principle of maximum ignorance posits that the coarse-grained description
of a system is maximally agnostic about its underlying microscopic structure.
We briefly review this principle for random matrix theory and for the
eigenstate thermalization hypothesis. We then apply this principle in
holography to construct ensembles of random mixed states. This leads to an
ensemble of microstates which models our microscopic ignorance, and which on
average reproduces the effective semiclassical physics of a given bulk state.
We call this ensemble the state-averaging ansatz. The output of our model is a
prediction for semiclassical contributions to variances and higher statistical
moments over the ensemble of microstates. The statistical moments provide
coarse-grained -- yet gravitationally non-perturbative -- information about the
microstructure of the individual states of the ensemble. We show that these
contributions exactly match the on-shell action of known wormhole
configurations of the gravitational path integral. These results strengthen the
view that wormholes simply parametrize the ignorance of the microstructure of a
fundamental state, given a fixed semiclassical bulk description.
