Now before I answer I want to emphasize that I think this sort of hypothetical tends to be actively misleading. Logically the hypothetical asks us to assume that the killer is guaranteed to avoid detection while in normal human discourse we usually round fairly small probabilities down to zero. Since the harm of people finding out about such a killing, particularly one motivated by this sort of cold seeming utilitarian calculus, is extremely high even a very very small probability of being caught makes the act wrong since there isn’t a correspondingly great benefit from killing him. Moreover, you would need to be confident (tho not as much) that this guy doesn’t have any normal habits that would make people believe his disappearance was the result of foul play and that you would never spill the beans nor be wracked by guilt for your action. In short in a modern urban environment no person will ever be in such a position.

However, if we imagine that someone who wouldn’t feel guilty over killing someone gets shipwrecked on a dessert island with literally no hope of rescue (say back before modern shipping) with a crewmate who becomes really depressed over the situation then a real person could be genuinely faced with this situation.

In either this case or the true logical hypothetical my answer is no, it isn’t immoral. However, the situations where murder is moral will be virtually non-existent in a modern society. Utilitarianism will differ radically with our intuitions in other cases just not in common realistic cases about whether to murder someone.

Now you might doubt that the harms from people knowing about the murder can really be that bad but that’s just because people are very bad at adding up the contributions from many small harms. The best way to see this is to ask about how much extra suffering and unhappiness there would be if murders and revenge killings were as bad here as they are in Iraq and then divide that badness by the difference in the murder rate.

I’ll argue for this position in a full post later.

Suppose there’s a homeless person nobody cares about wandering about the city. He is crazy and delusional: he believes he is invulnerable.

Due to my advanced ninja training, I would be able to kill him and dispose of the corpse without anybody noticing. If I do so, would I be doing something immoral, according to your conception?