Another type of ultimate disagreement between utilitarians, whether hedonistic or ideal, can arise over whether we should try to maximize the average… - J. J. C. Smart

The utilitarian’s ultimate moral principle...expresses the sentiment not of altruism but of benevolence, the agent counting himself neither more nor less than any other person. Pure altruism cannot be made the basis of a universal moral discussion because it might lead different people to different and perhaps incompatible courses of action, even though the circumstances were identical. When two men each try to let the other through a door first a deadlock results...Of course we often tend to praise and honour altruism even more than generalized benevolence. This is because people too often err on the side of selfishness, and so altruism is a fault on the right side. If we can make a man try to be an altruist he may succeed as far as acquiring a generalized benevolence.

Normally the utilitarian is able to assume that the remote effects of his actions tend rapidly to zero...It seems plausible that the long-term probable benefits and costs of his alternative actions are likely to be negligible or cancel one another out.
An obviously important case in which, if he were a utilitarian, a person would have to consider effects into the far future, perhaps millions of years, would be that of a statesman who was contemplating engaging in nuclear warfare, if there were some probability, even a small one, that this war might end in the destruction of the entire human race. (Even a war less drastic than this might have important consequences into the fairly far future, say hundreds of years.) Similar long term catastrophic consequences must be envisaged in planning flight to other planets, if there is any probability, even quite a small one, that these planets possess viruses or bacteria, to which terrestrial organisms would have no immunity.

I want to illustrate the relevance of metaphysics to ethics by reference to what is the greatest moral problem that has ever faced the human race: the question of nuclear war...the threat of nuclear war makes us envisage macro effects (effects on all people and the whole earth): the end of the human race, perhaps also of mammalian life itself, and the end of the prospect of humans evolving into yet higher and more wonderful forms of life...Those who comfort themselves with the thought that mutual deterrence has kept the peace for thirty years forget the importance of low probabilities in the macro context. Indeed what does it matter, from the perspective of possible millions of years of future evolution, that the final catastrophe should merely be postponed for (say) a couple of hundred years? Postponing is only of great value if it is used as a breathing space in which ways are found to avert the final disaster. And even a small probability that we shall not have this breathing space will yield negative expected utility of macro dimensions.