On one hand this is classed as selfless as using utilitarianism and the hedonic calculus is actually thinking of the best option for all people not just yourself or one specific person. Also, the golden rule is Love your neighbour as yourself which clearly means that you should bare everyone in mind and not be selfish and try to make everybody happy.
The theory recognises intelligence and the best decision not only for immediate consequences but long consequences. It is not selfish as all people are considered in the judgement and it takes time to make a decision by using the hedonic calculus. Utilitarianism is a much less selfish act than such theories as deontology, which thinks of whether an action is right or wrong all together rather than the people involved and their feelings. Whereas utilitarianism is a teleological approach.
On the other hand, utilitarianism is selfish as although it is acting on behalf of the majority, the minority still have to put up with the decision and therefore have to deal with the consequence. Act utilitarianism is a more selfish philosophy as it is based on the pleasure of those immediately affected and not on the consequence of people in the long run.
This is also a selfish theory as we are weighing out one persons happiness being more important than anothers; for example, if two people were dying and we could only save one, one was an old man and one a new born, we would have to save the new born as they have a longer future ahead of them, but this is still selfish as the old man will die, leaving his family distraught.
What if theres someone who is capable of feeling really, really, really intense happiness, just by kicking small children, not even very hard? It would seem that utilitarianism would support his right to kick such children, since the amount of displeasure he causes is easily outweighed by his own happiness.
Allowing that behaviour is selfish as somebody is still getting hurt even if it causing another person pleasure. Another example is killing someone not many people like, lots of people would be pleased at the death whereas hardly anyone would be bothered, this person is still getting killed and people are still being affected in a negative way, but according to utilitarianism killing this person is okay as it brings the majority happiness.