 Bronfman (2006, Other Internet Resources) observes that Joyce’s conditions on measures of inaccuracy do not determine a single measure, but rather a whole family of inaccuracy measures. All of Joyce’s measures agree that an agent whose degree of belief function violates the probability axioms should adopt a probabilistic degree of belief function which is at least as accurate in each, and more accurate in some, possible world. However, these measures may differ in their recommendation as to which particular probability measure the agent should adopt. In fact, for each possible world, following the recommendation of one measure will leave the agent less accurate according to some other measure. Why, then, Bronfman objects, should the ideal doxastic agent move from her non-probabilistic degree of belief function to a probability measure in the first place? Other objections are articulated in Maher (2002) and, more recently, in Easwaran and Fitelson (2012). These are addressed by Joyce (in 2009 and in 2013 (Other Internet Resources)) and Pettigrew (2013, 2016). Leitgeb and Pettigrew (2010a; 2010b) present conditions that narrow down the set of measures of inaccuracy to the so-called quadratic scoring rules. This enables them to escape Bronfman’s objection. For a detailed treatment, see the entry on  epistemic utility arguments for probabilism. 