There is a way to formulate preferentism so that the hypothesis that I desire to be badly off does not entail a contradiction.
(See Kagan (1998: 38) for a brief survey of the reasons.) And it looks like the paradox does not arise for ideal preferentism: it might be that if I were to undergo cognitive psychotherapy, I would not desire to be badly off. But I agree with Heathwood (2005) that none of the standard arguments for preferring ideal to actualist preferentism are any good.
Now suppose that in addition I have another intrinsic desire at t: a desire to be badly off, a desire that my welfare level at t be negative.
(P1) The scenario I described, in which someone has a certain set of desires, including the desire to be badly off, is a possible scenario.
Actualist preferentists who are willing to accept this account of what desire is can tell a similar story about the desire to be badly off. They can say that it is impossible (in some circumstances) for anyone to have that desire, and for that desire to be intrinsic.
I have said that preferentists who adopt this solution will say that it is impossible for someone to desire to be badly off, if that person also has certain other desires.
Preferentists who are bothered should say that no one can desire to be badly off, under any circumstances.
And, in fact, if we reject (P1) we cannot rest at saying that it is impossible to have an intrinsic desire to be badly off. (6) Suppose there are two people, A and B, and their only intrinsic desires are as follows: A desires that B be well-off, and B desires that A be badly off.
(Bradley (2007) rejects it for this reason.) Hedonists, for example, find all scenarios in which people desire to be badly off perfectly coherent.
Nevertheless, a response to the argument against preferentism that permits people to desire to be badly off (a response that accepts (P1) but rejects (P2)) avoids this controversy, and respects whatever pre-theoretic intuition we may have that it is possible to desire to be badly off.
Desires to be badly off create a problem for preferentism because they generate negative feedback in the "equation of welfare." The solution I am going to describe parallels solutions to other paradoxes involving a similar kind of negative feedback.
(I return to questions about what a general theory might look like in the conclusion.) For our purposes we only need to know how to determine the degree to which D, my desire to be badly off, is satisfied.
Above I showed how to derive a contradiction from preferentism and the possibility of a certain scenario in which I desire to be badly off. But that derivation assumed that my desire to be badly off was either satisfied or not satisfied; it took no account of degrees of satisfaction.
Plugging this value into the first equation, we find that (preferentists should say that in this scenario) my desire to be badly off is satisfied to degree 6/(M+10).
Recall how the paradox of desire was generated: introducing a second-order desire to be badly off led to negative feedback in the equation.