On a naive Humean picture of action, we have beliefs and desires and together these yield our actions.
But how do beliefs and desires yield beliefs? There are many (abstractly speaking, infinitely many, but perhaps only a finite subset is physically possible for us) maps from beliefs and desires to actions. Some of these maps might undercut essential functional characteristics of desires—thus, perhaps, it is impossible to have an agent that minimizes the satisfaction of her desires. But even when we add some reasonable restrictions, such as that agents be more likely to choose actions that are more likely to further the content of their desires, there will still be infinitely many maps available. For instance, an agent might always act on the strongest salient desire while another agent might randomly choose from among the salient desires with weights proportional to the strengths—and in between these two extremes, there are many options (infinitely many, speaking abstractly). Likewise, there are many ways that an agent could approach future change in her desires: allow future desires to override present ones, allow present desires to override future ones, balance the two in a plethora of ways (e.g., weighting a desire by the time-integral of its strength, or perhaps doing so after multiplying by a future-discount function), etc.
One could, I suppose, posit an overridingly strong desire to act according to one particular map from beliefs and desires to actions. But that is psychologically implausible. Most people aren’t reflective enough to have such a desire. And even if one had such a desire, it would be unlikely to in fact have strength sufficient to override all first-order desires—rare (and probably silly!) is the person who wouldn’t be willing to make a slight adjustment to how she chooses between desires in order to avoid great torture.
Nor will it help to move from desires to motivational structures like preferences or utility assignments. For instance, the different approaches towards risk and future change in motivational structure will still provide an infinity of maps from beliefs (or, more generally, representational structures) and motivational structures to actions.
Here’s one move that can be made: Each of us in fact acts according to some “governing mapping” from motivational and representational structures to actions (or, better, probabilities of actions, if we drop Hume’s determinism as we should). We can then extend the concept of motivational structure to include such a highest level mapping. Thus, perhaps, our motivational structure consists of two things: an assignment of utilities and a mapping from motivational and representational structures to actions.
But at this point the bold Humean claim that beliefs are impotent to cause action becomes close to trivial. For of course everybody will agree that we all implement some mapping from motivational and representational structures to actions or action probabilities (maybe not numerical ones), and if this mapping itself counts as part of the motivational structure, then everyone will agree that we all have a motivational structure essential to all of our actions. A naive cognitivist, for instance, can say that the governing mapping is one which assigns to each motivational and representational structure pair the action that is represented as most likely to be right (yes, this mapping doesn’t depend on the specific contents of the motivational structure).
Perhaps, though, a Humean can at least maintain a bold claim that motivational structures are not subject to rational evaluation. But if she does that, then the only way she can evaluate the rationality of action is by the action’s fit to the motivational and representational structures. But if the motivational structures include the actually implemented governing mapping, then every action an agent performs fits the structures. Hence the Humean who accepts the actual governing mapping as part of the motivational structure has to say that all actions are rational. And that’s a bridge too far.
Of course a non-Humean also has to give an account of the plurality of ways in which motivational and representational structures can be mapped onto actions. And if the claim that there is an actually implemented governing mapping is close to trivial, as I argued, then the non-Humean probably has to accept it, too. But she has at least one option not available to the Humean. She can, for instance, hold that motivational structures are subject to rational evaluation, and hence that there are rational constraints—maybe even to the point of determining a unique answer—on what the governing mapping should be like.