There are two types of alternative account. One alternative approach is, shall we say, deep: To desire something, on a deep account, is to be in some particular brain state or to have some underlying representational structure in the mind (perhaps the representation "I eat chocolate cake" in the Desire Box). The problem with such deep accounts is, I believe, that they don't get to the metaphysical root.
Consider an alien case. Suppose some Deep Structure D is necessary for wanting chocolate cake, on some deep account of desire. Unless that structure is more or less tantamount to possessing the dispositional profile constitutive (on my account) of wanting chocolate cake, then it should be metaphysically possible for an alien species that lacks Deep Structure D to act and react, inwardly and outwardly, in every respect as though it wanted chocolate cake. In such a case, I would suggest, both ordinary common sense and good philosophy advises ascribing the desire for chocolate cake to such hypothetical aliens, despite their lacking whatever Deep Structure D is necessary in the human case.
Alternatively, suppose some Deep Structure E is held to be sufficient for wanting chocolate cake. It seems that we could construct, at least hypothetically, a possible case in which Deep Structure E is present but the person in no way acts or reacts, inwardly or outwardly, like someone who wants chocolate cake: She wouldn't seek it, she wouldn't enjoy eating it, the anticipation of eating it would give her no pleasure, she gives it no weight in her plans, etc. It seems that we should say, in such cases, that the person does not desire chocolate cake. In ascribing desire or its lack, what we care about, both as ordinary folks and as philosophers, is how the person would act and react across a wide variety of possible circumstances. It is only contingently important what underlying mechanisms implement that pattern of action and reaction.
A second type of alternative approach is, like my own approach, superficial rather than deep, but unlike my approach it is narrow. What matters, on such accounts, is just some sub-portion of the pattern that matters on my approach. Maybe what is essential is that the person would choose the cake if given the chance, and not whether the person thinks she wants it or would feel anticipation when about to get it or would enjoy eating it. Or maybe what is essential is that the person judges that it would be good to get cake, and all the rest is incidental. Or maybe the essence is that receiving chocolate cake would be rewarding to that person. Or.... (See Tim Schroeder's SEP entry on Desire for a review of various narrow accounts, which Schroeder contrasts with holistic accounts like my own.)
The problem with narrow accounts is that it's hard to see a good justification for picking out just one feature of the profile as the essential bit. Desire is more usefully regarded as a syndrome of lots of things that tend to go together -- like extraversion is a syndrome, or like being happy-go-lucky is a syndrome. We can be liberal about what goes into the profile. It can be a cluster concept; aspects of the syndrome might be more or less central or important to the picture, but there need be no one essential piece that is strictly necessary or sufficient.
The flexible minimalism of a liberal, dispositional approach is, I think, nicely displayed when we consider messy, in-between cases. So let's consider one.
Matthew the envious buddy. Matthew and Rajan were pals in philosophy grad school. Ten years out, they still consider themselves close friends. They exchange friendly emails, comment warmly on each other’s Facebook posts, and seek each other for tête-à-têtes at professional meetings. In most respects, they are typical ageing grad-school best buddies. Also perhaps not atypically, one has had much more professional success than the other. Rajan was hired straight into a prestigious tenure-track position. He published a string of well-regarded articles which earned him quick tenure and, recently, promotion to full Professor. Now he is considering a prestigious job offer from another leading department. Matthew, in contrast, struggled through three temporary positions before finally landing a job at a relatively unselective state school. He has published a couple of articles and book reviews, suffered some ugly department politics, and is now facing an uncertain tenure decision. Understandably, Matthew is somewhat envious of Rajan – a fact he explicitly admits to Rajan over afternoon coffee in the conference hotel. Rajan is finishing his first book project and Matthew is halfway through reading Rajan’s draft.We can, of course, add as much detail to this case as we want -- dispositions pointing in different directions, in whatever balance we wish.
Matthew, as I’m imagining him, is not generally an envious character; he has a generous spirit. The well-wishes he utters to Rajan are sincerely felt at the time of utterance, not a sham. Picturing Rajan as the next David Lewis makes Matthew smile and chuckle with a good-natured shake of the head. There would be something truly cool about that, Matthew thinks – though the fact that he explicitly thinks that thought in that particular way already reveals a kind of ambivalence. Matthew intends to give Rajan his best advice about book revisions. He plans to recommend the book warmly to influential people he knows, including the program chair of the Pacific Division APA. At the same time, though, it’s true that were Matthew to read a devastating review of Rajan’s book, he would feel a kind of shameful pleasure, while seeing a glowing review in a top venue would bring a painful pang. In drafting out thoughts about the book, Matthew finds himself sometimes resentful of the effort, and he finds himself somewhat unhappy when he reads a particularly fresh and clever argument in the draft, wishing he had come up with that argument himself instead – though when he notices this about himself, he rebukes himself sharply. If Rajan’s book were to flop, Matthew would love commisserating; if Rajan’s book were to be a great success, that would add to the growing distance between the two friends. In some moments, Matthew admits to himself that he doesn’t really know if he wants the book to succeed or not.
Question: Does Matthew want Rajan's book to succeed?
The best answer, I submit, if we've built the case as I've intended, is "kind of", or "it's an intermediate, messy case". Just as someone might be an extravert in some respects and an introvert in other respects so that neither a plain ascription of "extravert" nor a plain ascription of "introvert" is quite right, so also with the question of whether Matthew wants Rajan's book to succeed. A liberal, dispositional approach to desire captures this ambivalence perfectly: Matthew wants the book to succeed exactly insofar as he matches the broad syndrome and no farther. There need be no "Q" either determinately in or determinately out of his "Desire Box"; there need be no one essential feature. In ascribing a desire, we are pointing toward a folk-psychologically recognizable pattern, and people might fit that pattern very well or not well at all, deviating in different ways and to different degrees.
The implications for self-knowledge of desire I leave as an exercise for the reader.
[For more on my dispositional approach to the attitudes see here.]