The Bayesian Who Knew Too Much

TL;DR

This paper discusses how imprecise credences can better represent ignorance within Bayesian frameworks, addressing issues raised by Norton regarding neutral evidence and improving handling of ignorance in probabilistic reasoning.

Contribution

It proposes that imprecise credences offer a Bayesian-compatible way to model ignorance, refining Norton's criteria for neutral support and addressing limitations in traditional Bayesianism.

Findings

Imprecise credences align with Norton's view of ignorance.

They provide a way to distinguish neutral from disconfirming evidence.

Reformulation of Norton's self-duality criterion is necessary.

Abstract

In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid inadequate neutral priors and better handle ignorance. The imprecise model generally agrees with Norton's representation of ignorance but requires that his criterion of self-duality be reformulated or abandoned.