In considering objections to desire utilitarianism, one class of objections that I have no concern with are those of the intuitionists.
An intuitionist objection would involve constructing some type of story in which desire utilitarianism might yield a conclusion that the reader is uncomfortable with. This story might involve a doctor with an opportunity to kill one patient to save five others, or a runaway trolley car that can be diverted from one track where it would kill five people onto another where it would only kill one person.
However, intuitionist arguments are really arguments from personal preference. The intuitionist is attempting to give rhetorical legitimacy to the inference from, "I do not like your conclusion and do not wish to accept it," to, "Therefore, you must be mistaken."
I do not consider merely a rhetorical way to give the appearance of legitimacy to an argument that effectively says, "Since I do not like your conclusion, your premises must be mistaken."
The argument has as much validity as arguing, "If your theories are correct, our sun will burn itself out in about five billion years. I don't like the idea that our sun will burn out. Therefore, your theories must be incorrect."
In order to raise an objection to desire utilitarian, the critic needs to provide evidence that some other type of reason for action actually exists. This requires more than an intuition. It requires a set of observations that the proposition, "desires are the only reasons for action that exist" cannot adequately explain. We would have to include additional reasons for action to explain those observations.
Again, this is the same model that physicists use with respect to postulating forces that exist. The criticism, "I don't like what your calculations predict about the motions of these bodies," does not work. However, the criticism, "According to your theories those bodies over there should be behaving in a particular way. However, when we look at them, we do not see them behaving that way. Therefore, your theories must be incorrect."
As it turns out, the desire utilitarian has no problem accounting for the "observations" that the intuitionists draw upon. They are explained by the likes and dislikes of the intuitionist himself. "You don't like the idea of a doctor killing a healthy patient to save five other patients."
In fact, with respect to these intuitions, the desire utilitarian can go one step further. After noting that the intuitionist has an aversion to a particular conclusion, he can then ask whether having such an aversion is a good thing or a bad thing. He would evaluate the aversion by asking whether, if that aversion were universal, it would tend to fulfill other desires or thwart other desires.
He can go beyond the fact that the intuitionist does not like a particular conclusion and ask, "What is the value of that particular dislike?"
Maybe it is a good idea to cause in people those aversions that make them dislike the idea of a doctor killing a healthy patient even to save five sick patients. After all, ridding doctors of this aversion would require reducing the overall aversion to killing generally. Any of our lives would be at risk the moment somebody feels it might be useful to end our life to promote some perceived social good. As such, a blanket prohibition on killing innocent people, even where (one believes) it would do some overall good, will tend to fill more desires than a moral permission to kill innocent people.
All of this fits, as it turns out, within a desire utilitarian theory of value. There is nothing here that provides the types of "observations" necessary to show that some other type of reason for action must exist.