You asked for a short description of desirism. I will give you three. The first two are aimed at school level albeit said slightly more technically and compactly than one would say to school kids. The third is a summary of the key points argued for in my previous letter. I will then finish this letter by answering your questions.
Desirism in in one line
Encourage desires that tend to fulfil other desires, discourage desires than ten to thwart other desires.
Desirism in a Couple of Paragraphs
If someone acts to thwarts one of your desires, this is undesirable to you, and this is the reason you have to discourage them from doing so. If you act to thwart one of their desires, that is undesirable to them, and that is the reason they have to discourage you from doing so. And the same goes for everyone else. Everyone uses praise and blame; and social reward and punishment to influence – to encourage and discourage - each other. One can also use other means to influence each other, such as physical and material threats, coercion and force. However we all have reason to discourage these these other means from being used on us, and others have the same reason from those means from being used on them.
Morality is about desires that are universally desirable to everyone, these are morally good desires and about desires that are universally undesirable to everyone, these are morally bad desires. So if we all encourage morally good desires – desires that tend to fulfil other desires, whoever has them - and discourage morally bad desires – desires that tend to thwart other desires , whoever has them - we make the world better for all of us, as we are all would better able to fulfil our own desires.
a Formal description of desirism
All value terms such as “good”, “bad”, “ought”, “ought not” are action-guiding, they are prescriptions.
The best pragmatic definition of a prescription is “there are reason to act of the kind to keep or bring about the state of affairs in question”.
A prescription is a type of description. It can be true or false. We use, metonymically, the label “good” for the “keep or bring about” relation and “bad” for the “stop or prevent “ relation. If these labels are applied to the other relation, then the prescription is false.
The other way a prescription can be false is if they refer to reasons to act that do not exist. The only reason to act that we know exist are desires – the only brain states that motivate us to act to keep or bring about states of affairs that are the targets of those desires.
Now we can use the label “fulfil” for the “kept or made” relation and the label “thwart” for the “stop or prevent” relation. Desires can also be directly fulfilled, or indirectly. So we can say an action “tends” to fulfil a desire, if it indirectly aids in bringing out the state of affairs that is the target of the desire.
So we can now say that good means “such as to fulfil or tend to fulfil the desires of the kind in question” and that “bad” means “such as to thwart or tend to thwart the desires of the kind in question” . We can also shorten this using “tend” to cover both direct and indirect fulfilment so that good (bad) means “such as to tend to fulfil (thwart) desires of the kind in question”.
Moral value terms are a specific type of prescription, they are universally prescriptive.
A universal prescription limits what kind of reasons to act apply in such a prescription. is that “there are reasons to act for everyone to keep or bring about the state of affairs in question”.
Given that the only reasons to act that exist are desires and that acts can only be modified by influencing desires, this means that only desires that tend to fulfil everyone’s desires and that are socially influenceable (malleable) are the kinds of desires amenable to be universally prescribed. Similarly only malleable desires that tend to thwart everyone’s desire are the kinds of desires amenable to be universally proscribed.
Combining this a true moral, that is universal, prescription or proscription is that there reasons to promote or demote the desire under evaluation, these reasons being whether the desire tends to fulfil or thwart everyone’s desires. If it does neither is is a morally neutral desires, not one of moral significance.
Your First Question
Since Desirism is sometimes called Desire Utilitarianism, does it agree that it is the outcome of an action that is important when determining its moral status and that an increase in the wellbeing, or reduction of suffering of sentient creatures, is the goal of moral actions?
A desire for wellbeing is only one possible desire. People can chose to fulfil a desire that sacrifices their wellbeing. We leave such a utility undetermined, allowing for it to be non-fungible, incommensurate and plural. Unlike traditional utilitarianism, Desirism does not impose one utility on everyone.
It is a consequentiality model, consequences do matter. The consequences being the material and physical affects on desires (more precisely on their fulfilment and thwarting). Actions are determined only indirectly, the evaluation focus is on desire and not acts and that takes better account of the results of empirical psychology.
In right act terms one could say that the right acts are acts that are the result of desires that tend to fulfil other desires, or the act that a person with desires that tend to fulfil other desires would perform.
Your Second Question
Does Desirism dictate that there is a right thing to do in any given situation, regardless of the culture in which it is taken? Are there, as Sam Harris contends, "many peaks on the moral landscape", or is there one rule for all?
Desirism is a means to establish what is universally desirable or not, independent of individual or group opinion. To establish matter of fact not opinion – culturally based or otherwise.
This is not to say it guarantees this result, some analysis may just be indeterminate. Also this is an empirical approach limited as is any other empirical approach to achieving the provisionally best conclusion given the available data. Further there can be disputes over the existing data e.g. which desires are affect or who has desires (such as over foetuses) as well as whatever conclusion being revisable in the light of new data. That is this is a provisional and defensible analysis.
Your Third Question
Are there grades of right and wrong rather than a binary decision?
Yes, one can compare two desires and it can be the case that one tends to fulfil more desire and tends to thwart less other desires, than another desire sunder evaluation. And so on.
Your Fourth Question
Does Desirism resolve the ought-is problem, or does it have nothing to say about this and just work from the principle that we ought to be moral and only concern itself with the "how" rather than the "why"?
The is-ought problem is not ignored by desirism. As noted above prescriptions are a type of description and can be true or false. There is no is-ought, description-dualism or fact-value dualism. That is an unempirical and (fallible) metaphysical claim.
This dualism can be shown to be false by showing that certain values or prescriptions can exist, rather than focus on others, where if they do not exist, then they are fictions. On that I assume we agreed.
One can only argue to “ought” conclusions if there is at least one “is” premise that contains one or more reasons to act that exist, then and only then one can draw ought conclusions. That is why desirism focused only on reasons to act that exists and so always refers to desires in arguing to ought conclusions.