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Utilitarianism is based on the principle of utility. Early utilitarians sometimes said that actions are good to the extent that they produce the greatest good or greatest happiness of the greatest number of people. Modern utilitarians believe that the principle of utility must be more complicated. Richard Brandt attempted to provide a more subtle formulation of the principle:

The principle with which we end is this: 'An act is right if and only if it conforms with that learnable set of rules the recognition of which as morally binding --roughly at the time of the act-- by everyone in the society of the agent, except for the retention by individuals of already formed and decided moral convictions, would maximize intrinsic value.'

Brandt goes on to add several comments on his version of the principle. In particular, he notes the following:

[I]f the proposed principle is correct, we can give at least a partial answer to a person who asks why he ought to perform actions he is obligated to perform, if they conflict with his self-interest. Perhaps a person who asks such a question is merely confused, and his query not worth our attention. But we can say to him that one reason for meeting his obligation is that by doing so he plays the game of living according to the rules which will maximize welfare. And this will be, at least partially, a satisfying answer to a man who is activated by love or sympathy or respect directed at other sentient beings generally.

Reference: From "Toward a Credible Form of Utilitarianism," reprinted in Contemporary Utilitarianism edited by Michael Bayles, p. 184-185. Brackets added.