On Imprecise Credences: The Jellyfish Guy Case, the Ellsberg Paradox and the Sleeping Beauty Problem

Abstract

The most common way of representing the strength of credences is by ascribing probabilities to them. Sharpers claim that credences can only be represented by precise probabilities. Non-sharpers, on the other hand, claim that credences may also be imprecise and should be represented by imprecise probabilities when the evidence is essentially imprecise (ambiguous, vague, conflicting or scarce). However, imprecise credences lead to irrational behaviour and do not make much sense when placed under scrutiny. I provide a coherence-based principle which enables me to defend the position of sharpers. This principle is then applied to three special cases, which are prima facie best explained by imprecise credences, i.e. the jellyfish guy case, the Ellsberg paradox and the Sleeping Beauty problem.