Situation A: 12-year-old Emma leads a happy life and gains U > 0 utility.

Situation B: Emma is continually raped and tortured for an online audience of consumers of sadistic child pornography. She loses L ≫ 0 utility. Each audience member gains 0 < ε ≪ L utility.

By the Archimedean property, there is some number of audience members N such that N·ε > L and even N·ε - L > U, namely N = ⌈(L + U + 1)/ε⌉. Thus, by simply increasing the number of audience members, B becomes preferable to A . This is true no matter how immense Emma's suffering or how negligible each audience member's enjoyment is.

This example seems to be a reductio against using aggregate utility as a basis for ethics. Has it been discussed in the literature? Which situation do you find preferable?

  • 2
    See Nozick's utility monster en.wikipedia.org/wiki/Utility_monster Jul 28, 2017 at 23:19
  • @AlexanderSKing Curiously, this example seems to be a counterpart of the utility monster, in the sense that it is a tyranny of a majority rather than a minority.
    – user76284
    Jul 28, 2017 at 23:23
  • 1
    There are certainly criticisms against utilitarianism in the literature. For this reason, who downvoted this would do well in explaining the reason for the downvote, please?
    – Rodrigo
    Jul 30, 2017 at 23:48
  • 1
    Myself, I have always taken these examples as counterexamples that demonstrate why aggregate utility is not a good model for determining "ethical" behavior. (In this case, defining "ethical" to be the kind of behavior I consider to be ethical today). It simply means that if someone provides an aggregate utility model defending an action, I need to take additional steps to determine if aggregate utility is applicable in that particular case.
    – Cort Ammon
    Aug 1, 2017 at 23:50

1 Answer 1


Rather getting emotional I would like to give my analysis in a rational way. Assuming ceteris paribus Situation B would be preferable. But .. In any legal system, the law is taken care in such a way that no innocent should be punished even if they have to let thousands of guilty or malignant go unpunished. The question is why so? Because in the given utility theory (by @user76284 ) holds good in a short term and in isolation, but if taken in the aggregate of all such crime (any unwanted act by mass) and long term there will create only chaos. [you can analyse the utility graph gain by Germans during Hitler regime in short term and long term due to action was taken by Him and there are many more examples.]. Given the choice, the first priority should be given to Win-Win over Loss-Win or obviously Loss-Loss, independent of the fact how small Gain is. You can get the same by Nash-equilibrium.

  • Thank you for your response. The legal system and "future crime" are immaterial to the thought experiment. I am curious, however. What makes you think situation B is preferable?
    – user76284
    Jul 31, 2017 at 13:10
  • No, I never thought about situation 2. Because personally, I don't believe in Majority bias. But if we just consider utility maximization(thinking only in black and white way) as you describe situation 2 will be preferable. But we also need to take judgment as such decisions are not black and while in nature but it's a gray area. Which makes situation 1 preferable as I explained.
    – Akhilesh
    Jul 31, 2017 at 16:00
  • Would you agree, then, that utility maximization is not always the ethical choice?
    – user76284
    Jul 31, 2017 at 18:45
  • @user76284 Yes, I Agree
    – Akhilesh
    Aug 1, 2017 at 3:40

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