The Bayesian Who Knew Too Much

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.