The defining feature of NU is that it puts zero intrinsic weight on positive experiences. If you have a theory that does include a preference for people to experience positive experiences, but just puts a higher weight on preventing suffering than it does on making people have positive experiences, then that theory is something different than negative utilitarianism. So it’d be clearer to call it something like a “suffering-focused” theory instead.
I think various people define NU differently.
Quoting Wikipedia: The term “negative utilitarianism” is used by some authors to denote the theory that reducing negative well-being is the only thing that ultimately matters morally. Others distinguish between “strong” and “weak” versions of negative utilitarianism, where strong versions are only concerned with reducing negative well-being, and weak versions say that both positive and negative well-being matter but that negative well-being matters more.
I think various people define NU differently.
Quoting Wikipedia: The term “negative utilitarianism” is used by some authors to denote the theory that reducing negative well-being is the only thing that ultimately matters morally. Others distinguish between “strong” and “weak” versions of negative utilitarianism, where strong versions are only concerned with reducing negative well-being, and weak versions say that both positive and negative well-being matter but that negative well-being matters more.
Fair enough, I hadn’t heard of the “weak NU” framing before. I’d still avoid it myself, though.