I saw a comment the other day by someone saying that he didn't think a coherent utilitarianism could be derived from John Stuart Mill's Utilitarianism. This seems a common sentiment. If it were true, I would say that it's so much the worse for utilitarianism, since my own view is that only Mill-style utilitarians are even serious contenders. But it is not, I think, true. The problem people have with Mill's account is that they read it with false assumptions about utilitarianism.
Utilitarianism is often characterized so as to suggest that we have an obligation to take that option which contributes to the greatest happiness of the greatest number. The key to understanding the coherence of Mill's utilitarianism is that Mill denies this. On Mill's account, we do not have an obligation to conform to the greatest happiness principle.
There are a number of reasons for this. Perhaps the simplest to grasp is that Mill is a positivist about obligation: on his account of obligation, obligations have to be created by imposing sanction. If there is no sanction imposed, there is no obligation. Short of affirming a divine command theory, however, which Mill certainly does not, this means that there are no natural obligations at all. We make our own obligations by education (cultivating conscience) or by public opinion or by law.
For Mill, the greatest happiness principle or principle of utility is not primarily concerned with obligation but practical reason. You can fail to conform to the greatest happiness principle without violating any obligations at all. The greatest happiness principle simply determines what is most reasonable. Failures to conform to the greatest happiness principle are less reasonable than they could be. Some such actions are unreasonable (or in the case of things we contemplate aesthetically, ugly, but this isn't discussed much in Utilitarianism), which is to say, there are lots of obvious options that would bring us closer to fulfilling the greatest happiness principle. But, of course, Mill has no interest in saying that stupidity is immoral. The greatest happiness principle is the primary standard for whether any of our plans are any good; but merely following a bad plan doesn't automatically make you morally wrong. In order to get to moral wrongness, he thinks we need to introduce sanction. Those things are morally wrong that are so unreasonable (according to the greatest happiness principle, as far as we can see that it applies) that it would be reasonable (according to the greatest happiness principle, as far as we can see that it applies) for us to punish those who did them, leading us actually to punish those who did them (by guilt, shaming, or legal punishment).
This has a number of implications for Mill's system. It's why our typical moral rules need to be respected (Mill places an immense amount of importance on doing one's duty), but also why they can be improved upon. It's why we can have conflicting duties (since the obligation derives not from the principle of utility itself but from how we go about sanctioning it, and in particular cases, even if we are being purely reasonable, what we are sanctioning in one way might interfere with what we are sanctioning in a different way). It's why he sometimes sounds like a rule utilitarian and sometimes like an act utilitarian -- one of the reasons why, anyway. It's why he thinks the principle of utility hardly needs much defense at all, since he thinks we all implicitly appeal to it whenever we make any plans or decisions at all. It is a significant factor in his divergence from Bentham, and is part of why Mill can hold that Bentham is right as far as he goes and yet also fatally incomplete. It goes part of the way to giving us an answer of why Mill thinks the principle of utility is consistent with the principle of harm he gives in On Liberty. And it is a necessary precondition for the Art of Life that he lays out in System of Logic.
This is not to say that there aren't issues that could be raised when it comes to Mill's utilitarianism. But the basic structure is quite coherent when you realize that we aren't morally required to conform to the greatest happiness principle itself.
