  We use Bayesian model selection tools to forecast the Planck satellite's
ability to distinguish between different models for the reionization history of
the Universe, using the large angular scale signal in the cosmic microwave
background polarization spectrum. We find that Planck is not expected to be
able to distinguish between an instantaneous reionization model and a
two-parameter smooth reionization model, except for extreme values of the
additional reionization parameter. If it cannot, then it will be unable to
distinguish between different two-parameter models either. However, Bayesian
model averaging will be needed to obtain unbiased estimates of the optical
depth to reionization. We also generalize our results to a hypothetical future
cosmic variance limited microwave anisotropy survey, where the outlook is more
optimistic.
