Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist

Abstract

This article considers a puzzling conflict between two positions that are each compelling: ( a ) it is irrational for an agent to pay to avoid ‘free’ evidence, and ( b ) rational agents may have imprecise beliefs. An important aspect of responding to this conflict is resolving the question of how rational (imprecise) agents ought to make sequences of decisions—we make explicit what the key alternatives are and defend our own approach. We endorse a resolution of the aforementioned puzzle—we privilege decision theories that merely permit avoiding free evidence over decision theories that make avoiding free information obligatory.