When Ignorance is Bliss
This challenges conventional wisdom in decision-making and statistics, offering insights for practitioners dealing with uncertainty, though it appears incremental as it builds on existing frameworks.
The paper argues that ignoring information can be beneficial in certain prediction tasks when uncertainty is represented by a set of probability measures, showing that it avoids uncertainty increase in non-Bayesian analysis and improves predictions for small sample sizes in Bayesian analysis.
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.