Utilitarianism sounds like a good idea. After all, it makes sense to seek the greatest good!

Well, no. Here's a thought experiment that shows how utilitarianism would make you perform an obviously unethical act. I've no attribution for this, but it certainly isn't mine. The subject matter of the paper is, I think, the difference between killing and letting die.

You're the head of a hospital in some remote area. In 5 separate wards, you have 5 different patients waiting for transplants of 5 different organs. If you don't do a transplant tonight, each patient will die. If you do the transplant, they'll live (you can make it more realistic by giving each a 95% chance of survival; it doesn't change the argument). The 5 patients are 5/6ths of an identical sextuplet, between which you can transplant (no, this is not a very realistic scenario). And you have no organs.

Until sextuple #6 walks in, complaining of a slight headache, and asks for an aspirin.

Choices

  1. Give sextuple #6 an aspirin. Result: 1 person lives, the other 5 die.
  2. Take the opportunity to "cannibalise" sextuple #6 for "spare parts" (organs for the transplants). Result: 1 person dies, the other 5 live (if you're still with the 95% chance of survival, that's an expected utility of 1 dead person and 5.7 live ones).
Which do you pick?

Option #1, I sincerely hope. And before you go about complaining the whole scenario is impossible, consider that if you pick #2, you're willing to kill a person whenever their organs are compatible with 2 recipients.

What gives? Evidently you make ethical judgements based on principles other than utilitarianism.