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I want to add some more about Hare's approach to utilitarianism because I think the he was one of its most knowledgeable advocates.

Hare believed that moral concepts implied a kind of necessary universalization. If we used a moral concept such as 'ought' in a moral judgement such as "Jones ought to help his mother," then it logically followed that anyone in the same position as Jones ought to help his mother. This logically required universalization implied that we could not be partial to ourselves or to anyone else in making moral judgments. More importantly, Hare believed that the universalization requirement helped us formulate an argument for moral utilitarianism. Here's what he said:

Though unable, because of the difficulties interior to utilitarian theory, to state clearly and exactly what kind of utilitarianism if any will emerge, if the method of argument which I have outlined is developed to cover multilateral situations, I wish merely to point out that the logical character of moral language, as I have claimed it to be, is the formal foundation of any such theory. It is in the endeavour to find lines of conduct which we can prescribe universally in a given situation that we find ourselves bound to give equal weight to the desires of all parties (the foundation of distributive justice); and this, in turn, leads to such views as that we should seek to maximize satisfactions. For if my action is going to affect the interests of a number of people, and I ask myself what course of action I can prescribe universally for people in just this situation, then what I shall have to do, in order to answer this question, is to put myself imaginatively in the place of the other parties (or, if they are many, of a representative sample of them) and ask the same sort of questions as we made the creditor ask when he had imagined himself in the situation of his debtor. And the considerations that weigh with me in this inquiry can only be, How much (as I imagine myself in the place of each man in turn) do I want to have this, or to avoid that? But when I have been the round of all the affected parties, and come back, in my own person, to make an impartial moral judgement giving equal weight to the interests of all parties, what can I possibly do except advocate that course which will, taken all in all, least frustrate the desires which I have imagined myself having? But this (it is plausible to go on) is to maximize satisfactions. [R. M. Hare, Freedom and Reason, p. 122-3.]