• I’m not sure how negative utilitarianism changes things. Positive and negative utilitarianism are equivalent whenever UFs are bounded and there are no births or deaths as a result of the decision.

Negative utilitarianism interprets this situation as the sadists suffering from boredom which can be slightly alleviated by knowing that the guy they hate is suffering.

• You might be correct, but I’m not convinced that all negative utilitarians would agree with you. I think that some formulations (e.g. potentially NHU as described here) would describe the person not getting tortured as producing a reduction in pleasure for the sadists, and thus not ascribe any moral value to the sadists’ preferences not getting fulfilled.

I’d be curious to read more about your comment that “Positive and negative utilitarianism are equivalent whenever UFs are bounded and there are no births or deaths as a result of the decision.” Do you have some resources you could link for me to read?

• I’m referring to the fact that utility functions are equivalent under positive affine transformations (if you add a constant and multiply it by a positive constant, the UF remains the same in the sense that it has the same preference in every situation)

Assuming we are computing the utility of an outcome by assigning a utility to each person and then summing them, adding a constant value to any person’s utility doesn’t change the comparison between outcomes, because the net effect is just to add a constant to the utility of each outcome(as long as the person we are adding a constant value to exists in every outcome).

Therefore, we can convert the situation to negative utilitarian without functionally changing it, by subtracting the maximum utility from each person, ensuring that everyone’s utility will be negative in every outcome. We can also convert it to positive utilitarian by subtracting the minimum in a similar way.

This analysis assumes that there is a maximum and a minimum utility, and that every outcome has the same set of people in it, so if these assumptions break there may be relevant differences.

• Okay I see what you’re saying here. But do you think that that a substantial number of negative utilitarians would agree with that argument? I don’t think they would, because I think integral to many conceptions of negative utilitarianism is the idea that there’s a qualitative difference between suffering and lack of pleasure.

• Okay, maybe the NUs wouldn’t interpret the problem as I phrased it in this way, but the problem can be slightly changed to have a similar conclusion, by saying that the sadists are mildly annoyed when the guy isn’t being tortured, instead of wanting it for their pleasure.