By "Psychological Hedonism" I mean not that theory which originally went under under this name, to the effect that we each do we believe to be most in our interests. Assuming (what may not be true) that we are fully aware of our beliefs, that doctrine is so patently in contradiction of the facts that it is amazing that a man of Bentham's intellectual calibre would believe it. A demonstration of that theory's falsity would be quite redundant.
The theory I would question is the more modern one, to the effect that we each act in whatever manner we most like (or, perhaps, what we most like the idea of). Again, the issue must be raised of whether we are fully aware of what it is that we like or dislike, and I would say not. But this is not, of itself, fatal to the theory, for it only relates our actions to our likes while saying nothing of our awareness (or otherwise) of them. The theory could survive by assuming that even those likes we are unaware of influence our behaviour. (The theory could be interpreted as meaning that we always do what we are aware of liking the most, however it would then be scarcely more credible than Bentham's version.)
The main line of attack against this psychological hedonism would be this: in light of the evidence [give some sources here], we shall have to admit that the brain consists of several parts, which are quite distinct from and fairly independent of each other. The potential error occurs in assuming that the capacity of each part to influence our behaviour is in proportion to its capacity for liking and disliking.
An illustration: assume the brain has two relevant parts (i.e. capable of liking and disliking), A and B. Part A likes a certain course of action, but only mildly (compared to inaction). Part B intensely dislikes that course of action (again, compared to inaction). Psychological hedonism would therefore seem to indicate that, since the sum of the feelings is negative, the act shall not be performed (i.e. inaction will be preferred). This may be mistaken in that part A may be better connected to whichever part of the brain (C) that actually directs the muscles. Part B may be relatively disconnected from C, and therefore relatively impotent to direct our behaviour.
The actual system would have to be modelled as a weighted sum, where each term in the summation is the product of one brain-part's intensity of like or dislike for the act and that brain-part's action-guiding potency. Once these weights are accounted for, it is clear that someone may act a certain way despite - on balance - disliking it more than an available alternative.