  We propose a simple method to quantify a possible exclusion of the inverted
neutrino mass ordering from cosmological bounds on the sum of the neutrino
masses. The method is based on Bayesian inference and allows for a calculation
of the posterior odds of normal versus inverted ordering. We apply the method
for a specific set of current data from Planck CMB data and large-scale
structure surveys, providing an upper bound on the sum of neutrino masses of
0.14 eV at 95% CL. With this analysis we obtain posterior odds for normal
versus inverted ordering of about 2:1. If cosmological data is combined with
data from oscillation experiments the odds reduce to about 3:2. For an
exclusion of the inverted ordering from cosmology at more than 95% CL, an
accuracy of better than 0.02 eV is needed for the sum. We demonstrate that such
a value could be reached with planned observations of large scale structure by
analysing artificial mock data for a EUCLID-like survey.
