Utilitarianism Endorses Gang Rape
Number of rapists increases linearly while the suffering of the victim increases only parabolically
Decreasing Marginal Utility
It is a fact that everything pleasurable has decreasing marginal returns. The first potato chip is delicious. The next one slightly less so, and the 30th potato chip is not even close to as satisfying as the first one was. Unpleasant things exhibit this phenomenon as well with decreasing marginal badness. If you were enslaved in a factory for one day it would be unpleasant, but additional days thereafter would be less unpleasant than the first. Another way to say this is that the negative utility of the change from zero days in the factory to 1 day in the factory is a lot less than the negative utility of the change from 10 days in the factory to 11 days in the factory.
This is one of the fundamental facts of economics and it’s also just a well-known fact about human nature. As you continue to get more of a good thing, each increment is feels less good, and if you continue to get more of a bad thing, each increment feels less bad.
The Utilitarian Gang
There are some men who have never been able to attract a woman to have sex with. For those people, if they were able to have sex one time next week, it would be very valuable to them. They would value that opportunity more highly than a man who has plenty of sexual opportunity would.
A woman who is gang raped by two men has a very negative experience. Gang rape by three men is also very bad, but it is clearly less than 150% as bad as gang rape by two men. Going from no rape to rape by one man is a way bigger deal than going from rape by one man to rape by two men. Going from two men to three men is also bad, but a smaller increment of badness than going from one man to two men. In other words, the experience has decreasing marginal badness. The amount of badness produced by the addition of each new rapist added to the gang rape is less than the marginal badness produced by the previously added rapist.
However, for each rapist, the gang rape is a new, one time experience. Ten rapists experience ten times as much pleasure as one rapist.

The total pleasure experienced by all the rapists increases linearly in the number of rapists but the displeasure/pain experienced by the victim increases only parabolically in the number of rapists.
Conclusion
Since Utilitarianism posits that the right thing to do is the thing that maximizes pleasure - without regard to rights, fairness or justice, one first-blush objection to Utilitarianism is that it seems to imply that hurting people is good so long as the aggressor enjoys hurting people more than the victim dislikes being hurt.
The Utilitarian reply is that such a situation basically never happens in real life. In all ordinary cases, a person dislikes being beat up more than a bully likes beating them up. A person dislikes being murdered more than the murderer enjoys the murder. A person dislikes being raped more than the rapist enjoys the rape. Utilitarians say that this asymmetry between being being hurt and hurting others is a fundamental part of human experience, and the reason that we intrinsically think it’s wrong to hurt others is because we are all familiar with the basic fact that being hurt is much worse than whatever satisfaction you get by hurting others.
For one on one interactions, that Utilitarian response is correct. But it breaks down when you consider interactions between one person and several people. Even if the pleasure experienced by each individual aggressor is less than the suffering of the victim, the total pleasure experienced by all aggressors could be greater than the victim’s suffering.
This is not a sci fi scenario. There are a large number of sexually unsuccessful men and a sufficiently large number of them could experience enough total pleasure to outweigh the displeasure/pain of a single victim.
This is a devastating objection to Utilitarianism. Utilitarianism says that gang rape by sexually unsuccessful men is morally ok, and even morally good. Libertarianism and other forms of Deontology say that gang rape is morally wrong because it violates fundamental rights.
And here’s another hypothetical: raping the unconscious. Remember that French guy who drugged his wife and let other guys rape her? Most of us think this is abhorrent and that almost no punishment would be severe enough for him.
But to the utilitarian, it was just fine, at least until she found out. After all, she didn’t know and therefore suffered no distress. And all those guys got pleasure! So maybe he added utility to the world!
Now if he’d done something really evil, like eating shrimp, we could clamp down on him.
Several advanced civilizations from the middle east seem to have used the deductive reasoning gained from their philosophical golden age to work this one out