The differences between act-, rule-, and motive utilitarianism.
Act-, rule- and motive utilitarianism could appear to be quite different theories: rule- and motive utilitarianism seem at first to be more sophisticated forms, which answer some of the criticisms that plague act-utilitarianism. However, upon analysis the distinctions between these theories appear to break down: if rule- and motive utilitarianism are to have adequate justification then they must collapse back into merely a sophisticated theorem of act-utilitarianism. Indeed, Frey gives a formulation of act-utilitarianism such that it has many similarities with both rule- and, especially, motive utilitarianism, whilst deriving this solely from the basic act-utilitarian principle.
Classical act-utilitarianism, as propounded by Bentham and Mill, is a normative ethical theory based on three tenets: consequentialism; the principle of equity and psychological hedonism. It is consequentialist because it takes the rightness of actions to be determined only by their consequences: actions have instrumental, not intrinsic value. From the theory of psychological hedonism, that people naturally desire pleasure/happiness and shun pain, it is assumed that pleasure is the good, and the ultimate end of human action. The principle of equity states that all persons should be considered as equal when assessing the distribution of pleasure; your pleasure is exactly as valuable as anyone else's. Classical act-utilitarianism thus states that a morally good action is one which maximises pleasure and minimises pain for all those affected by the act. Thus no action, even murder, is inherently wrong: to decide what a good action is one must weigh up the balance of pleasure over pain. Thus Truman, when deciding to use atomic weapons in the second world war, was essentially making a utilitarian decision: many lives were lost, but this was done in order to prevent the war continuing, potentially losing even more lives. There are many criticisms which can be levelled at this form of utilitarianism, which is why it is not favourable among modern philosophers. Psychological hedonism is generally considered to have been refuted as a theory, and utilitarianism now generally refers to any consequentialist welfarist theory; a good utilitarian action is one which maximises net human welfare. Human welfare is taken to mean different things by different types of utilitarianism, such as preference or ideal utilitarianism, but for the purposes of discussing the differences between act-, rule- and motive utilitarianism these do not matter.