Does the desirability of a proposition depend on whether it is true? Not according to the Invariance assumption, held by several notable philosophers. The Invariance assumption plays an important role in David Lewis’ famous arguments against the so-called Desire-as-Belief thesis (DAB), an anti-Humean thesis according to which a rational agent desires a proposition exactly to the degree that she believes the proposition to be desirable. But the assumption is of interest independently of Lewis’ arguments, for instance since both Richard Jeffrey (...) and James Joyce make the assumption (or, strictly speaking, accept a thesis that implies Invariance) in their influential books on decision theory. The main claim to be defended in this paper is that Invariance is incompatible with certain assumptions of decision theory. I show that the assumption fails on the most common interpretations of desirability and/or choice-worthiness found in decision theory. I moreover show that Invariance is inconsistent with Richard Jeffrey’s decision theory, on which Lewis’ arguments against DAB are based. Finally, I show that Invariance contradicts how we in general do and should think about conditional desirability. (shrink)