  Recent works combining neutrino oscillation and cosmological data to
determine the neutrino hierarchy found a range of odds in favour of the normal
hierarchy. These results arise from differing approaches to incorporating prior
knowledge about neutrinos. We develop a hierarchy-agnostic prior and show that
the hierarchy cannot be conclusively determined with current data. The
determination of the hierarchy is limited by the neutrino mass scale
$\Sigma_{\nu}$ measurement. We obtain a target precision of
$\sigma(\Sigma_{\nu}) = 0.014$ eV, necessary for conclusively establishing the
normal hierarchy with future data.
