When Ignorance is Bliss

TL;DR

This paper challenges the common belief that more information always improves decision-making, demonstrating that ignoring certain information can be beneficial in specific uncertain scenarios, especially with small samples.

Contribution

It introduces a formal analysis showing when ignoring information is advantageous within set-based uncertainty models, contrasting Bayesian and non-Bayesian perspectives.

Findings

Ignoring information can prevent dilation of uncertainty.

Bayesian methods may perform worse with small samples when ignoring information.

In certain cases, ignoring information leads to better predictions.

Abstract

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.