 The first objection to the application of  Naive Dominance  in the context of the accuracy argument for Probabilism was first stated in an unpublished manuscript by Aaron Bronfman entitled “A Gap in Joyce’s Proof of Probabilism”; it has been discussed by Hájek (2008) and Pettigrew (2010, 2013b). The starting point for the objection is the observation that  Credal Veritism  and  Joycean Inaccuracy  do not together narrow down the class of legitimate measures of epistemic disutility to a single function; they characterize a family of such measures. But, for all that  Theorem 4  (Joyce’s Main Theorem) tells us, it may well be that, for a given non-probabilistic credence function \(c^*\), different measures in this family of legitimate inaccuracy measures give different sets of credence functions that accuracy dominate \(c^*\). Thus, an agent with a non-probabilistic credence function \(c^*\) might be faced with a range of credence functions, each of which accuracy dominates \(c^*\) relative to a different legitimate inaccuracy measure. Moreover, it may be that any credence function that accuracy dominates \(c^*\) relative to Joycean inaccuracy measure \(\mathfrak{I}\) does not accuracy dominate \(c^*\) relative to the alternative Joycean measure \(\mathfrak{I}'\); indeed, it may be that any credence function that dominates \(c^*\) relative to \(\mathfrak{I}\) risks very high inaccuracy at some world relative to \(\mathfrak{I}'\), and vice versa. In this situation, it is plausible that the agent is rationally permitted to stick with her non-probabilistic credence function \(c^*\).