 Now, relative to \(\mathfrak{B}'\), \(c^*\) is indeed accuracy dominated by \(c'\) and \(c'\) is not accuracy dominated by \(c^\dag\). But \(c'\) is accuracy dominated by \(c^+\) defined on \(\mathcal{F}^+ = \{\top\}\), where \(c^+(\top) = 1\), since the average Brier score of \(c^+\) is \(\frac{1}{1}|1-1|^2 = 0\) at all worlds, while the average Brier score of \(c'\) is \(\frac{1}{2}(|1-0.5|^2 + |0-0.5|^2) = 0.25\) at all worlds. Jennifer Carr (2015) initiated the investigation into how epistemic utility arguments for Probabilism might work when we start to compare credence functions defined on different sets of propositions. She notes the analogy with population axiology in ethics (see entry on  the repugnant conclusion).  Pettigrew (2018b) takes this analogy further, proving an impossibility result analogous to those prevalent in that part of ethics.