  It is commonly-accepted wisdom that more information is better, and that
information should never be ignored. Here we argue, using both a Bayesian and a
non-Bayesian analysis, that in some situations you are better off ignoring
information if your uncertainty is represented by a set of probability
measures. These include situations in which the information is relevant for the
prediction task at hand. In the non-Bayesian analysis, we show how ignoring
information avoids dilation, the phenomenon that additional pieces of
information sometimes lead to an increase in uncertainty. In the Bayesian
analysis, we show that for small sample sizes and certain prediction tasks, the
Bayesian posterior based on a noninformative prior yields worse predictions
than simply ignoring the given information.
