It is well known that complete prior ignorance is not compatible with
learning, at least in a coherent theory of (epistemic) uncertainty. What is
less widely known, is that there is a state similar to full ignorance, that
Walley calls near-ignorance, that permits learning to take place. In this paper
we provide new and substantial evidence that also near-ignorance cannot be
really regarded as a way out of the problem of starting statistical inference
in conditions of very weak beliefs. The key to this result is focusing on a
setting characterized by a variable of interest that is latent. We argue that
such a setting is by far the most common case in practice, and we show, for the
case of categorical latent variables (and general manifest variables) that
there is a sufficient condition that, if satisfied, prevents learning to take
place under prior near-ignorance. This condition is shown to be easily
satisfied in the most common statistical problems.Comment: 15 LaTeX page