David Lewis argues against an anti-Humean toy theory on which the value of a proposition A is the agent's credence in the proposition Av which says that A is valuable. Thus: V(A)=C(Av) where C is credence. His argument depends crucially on the independence assumption that the value of A doesn't depend on whether A is true:
But independence understood this way is plainly false. Suppose my initial valuation of my daughter making dessert (D) is V(D)=C(Dv)=1/2. But suppose I completely trust her judgments of value, she had informed me that she made dessert if and only if making dessert was valuable, and this was all in the background knowledge. Then obviously my valuation of D had better change upon learning whether D is true. If D is true, then her making dessert was valuable; if not, it wasn't. Thus: C(Dv|D)=1 and C(Dv|~D)=0, contrary to (1).