(BDI) People always act so as to fulfill their most and strongest desires, given their beliefs.
But this is either trivial or false.
It is trivial if we weight desires according to their eventual behavioural impact, so that BDI stipulatively defines 'desire'. But this is rather pointless, since it means that we cannot tell what desires someone has until we see which act they perform. (And if their decision is highly sensitive to trivial situational changes, as seems likely, then desires would seem not to have any stable prior existence.) So it seems like a bad definition. In any case, interesting truths cannot be arrived at by mere stipulation.
If we want BDI to be a substantive thesis, it must invoke some independent notion of desire (strength). The most obvious contender here is the felt strength of a desire in our conscious phenomenology. But then BDI is simply false: we are not always bound to follow that which most tempts us -- the will may override mere feelings.
Finally, there is the (more morally important) dimension of reflective endorsement, where we may more naturally speak of 'ends' than 'desires'. But again, this interpretation renders BDI false: unfortunately, we do not always pursue those ends we believe to be best. We may be waylaid by mere (unendorsed) desires.
This distinction is captured rather nicely in Sidgwick's Methods of Ethics (1890). The suggestion that "adoption of an end means the preponderance of a desire for it" - precluding the possibility of instrumental irrationality - is due, he suggests, to "a defective psychological analysis" (p.39):
According to my observation of consciousness, the adoption of an end as paramount -- either absolutely or within certain limits -- is quite a distinct psychical phenomenon from desire: it is to be classed with volitions, thought it is, of course, specifically different from a volition initiating a particular immediate action.